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THE 


True  Order  of  Studies. 


REV.  THOMAS  HILL,  D.D., 

Formerly  President  of  Harvard  Univrsity,  author  of  "  Geometry  and 
Faith,''''  i£tc..  Etc. 


NEW  YORK 
G.    P.    PUTNAM'S    SONS 

27  AND  2g  West  2  3D  Street 

1SS6 


Copyright : 

O.  P.  PUTNAM'S  SONS 

1875. 


165  5^ 
PREFACE. 


THE  hierarchy  of  sciences  adopted  as  the  basis 
of  this  work,  was  first  perceived  by  me  one  night 
about  the  first  of  February,  1843,  while  attempting  to 
answer  a  chance  question.  Four  years  afterwards  I 
began  to  use  it  as  the  basis  of  lectures  on  a  revised 
scheme  of  Common  School  Education,  nearly  identical 
with  that  presented  in  this  volume.  In  May,  1853, 
the  hierarchy  was  first  published  in  an  address  deliver- 
ed before  the  Harvard  Natural  History  Society.  I 
used'  it  in  a  P.  B.  K.  address  at  Cambridge,  in  1S59  ; 
and  have,"^ince  that  time,  used  it  repeatedly  in  address- 
es, lectures,  and  magazine  articles,- and  especially  in  a 
series  of  four  communications  to  Barnard's  Journal 
of  Education  for  1859,  bearing  the  same  title  as 
this  book. 
Portland,  Me.  August,  187^ 


CONTENTS. 


CHAPTER  PAGE 

Preface 5 

I.— The  Child 7 

II. — The  Hierarchy  of  Sciences 11 

III. — Geometry 24 

IV. — Arithmetic 39 

V. — Algebra , 51 

VI. — Physics 54 

VII. — Chemistry 65 

VIII. — Mineralogy 69 

IX. — Physiology 71 

X. — Botany 74 

XI. — Zoology 79 

XII. — Geology gr 

XIII. — Commodity 94 

XIV.— Art 99 

XV. — Language 103 

XVI.— Law i?3 

XVII. — Political    Economy 127 

XVIII.— Psychology 13-1 

XIX. — Aesthetics 134 

XX. — Ethics 139 

XXI. — Theology 142 

XXII— Scholia 149 

XXIII. — A  Curriculum 159 


THE 


TRUE    ORDER    OF    STUDIES. 


CHAPTER  I. 

THE  CHILD, 


A  THOROUGH  and  complete  education  ought  to 
preserve  and  increase  the  pupil's  bodily  health 
and  strength  ;  give  him  command  of  his  own  muscu- 
lar, and  mental  powers  ;  increase  his  quickness  in  per- 
ceiving through  his  five  senses,  and  quicken  his  men- 
tal perception  ;  form  in  him  the  habit  of  prompt  and 
accurate  judgment ;  lead  to  delicacy  and  depth  in 
every  right  feeling ;  and  make  him  inflexible  in  his 

^     conscientious  and  steadfast  devotion  to  all  his  duties. 

^     In  other  words  an  integral  education  must  include  at 
least  these  four  branches  : — gymnastics,  or  care  of  the 

'^    body  ;  noetics,  or  training  of  the  mind  ;  aesthetics,  or 

rj  cultivation  of  the  tastes  ;  and  ethics,  which  shall  include 
religion  as  well  as  duty.  And  in  every  part  of  each 
branch  of  education,  there  will  be  a  double  end  in  view, 
namely,  the  increase  of  knowledge,  and  the  increase 
of  skill.     Each   study  may  be  made  the  object  of 


8  TRUE    ORDER    OF    STUDIES, 

thought,  or  the  object  of  action  ;  in  the  one  case  it  i3 
pursued  as  a  science  ;    in  the  other  case  as  an  art. 

In  the  present  little  book,  I  occupy  myself  chiefly 
with  the  second  branch,  the  education  of  the  intellec- 
tual powers  ;  not,  by  any  means,  because  I  consider  it 
as  more  important  than  the  others  ;  but  simply  be- 
cause I  have  something  to  say  upon  it. 

The  intellectual  powers  may  be  roughly,  but  con- 
veniently divided  into  three  groups,  the  perceptive,  the 
imaginative,  and  the  reflective. 

By  perception  I  mean  the  direct  vision  of  truth, 
whether  by  outward  or  by  inward  sense.  By  the  five 
senses  we  have  a  direct  perception  of  the  presence  of 
colors,  sounds,  odors,  flavors,  variations  of  temperature, 
and  other  tangible  and  visible  things.  By  the  inter- 
nal powers  of  consciousness  we  have  a  direct  percep- 
tion of  our  own  feelings,  and  know  that  we  love,  hate 
fear,  are  glad  or  sad ;  and  by  internal  sense  we  also 
know  the  existence  of  space,  time,  power,  thought. 

By  imagination  I  mean  the  reproduction,  or  imita- 
tion, in  the  mind,  of  the  impressions  previously  made 
by  direct  perception.  When  imagination  is  confined 
to  a  simple  reproduction  of  the  impressions  made  in 
perception,  it  is  usually  called  memory  ;  and  the  term 
imagination  is  by  most  persons  confined  to  the  cases  in 
which  the  remembered  impression  is  variously  modi- 
fied, or  merely  imitated.  The  word  fancy  is  by  many 
writers  applied  to  the  cases  in  which  the  imagination  is 
occupied  with  inventing  imitations  of  external  things, 
and  the  word  imagination  confined  to  inventions  of 
character  or  of  spiritual  attributes. 


THE   CHILI).  y 

By  reflection  I  mean  the  act  of  comparing,  by  help 
of  the  imagination,  the  truths  of  perception,  or  the 
creations  of  the  imagination.  When  this  comparison 
of  truths  elicits  new  truths  of  relation,  between  the 
compared  truths,  it  is  called  reasoning.  Thus  reason- 
ing may  be  considered  as  an  art  of  bringing  truths  into 
a  position  to  be  perceived  by  the  internal  sight. 

It  may  be  observed  that  the  words  imagination 
reason,  and  perception,  are  also  used  to  denote  the 
faculties  of  the  mind  by  which  we  perform  the  acts  of 
imagination,  reasoning,  and  perception. 

The  first  act  of  the  mind  must  always  be  the  direct 
perception,  of  some  truth,  as  the  necessary  prelude  to 
any  act  of  reason  or  imagination.  In  the  history  of 
any  child's  intellectual  development  it  is  always  the 
case,  also,  that  his  powers  of  external  perception  give 
the  earliest  evidence  of  activity.  For  the  first  seven 
years  of  his  life,  his  chief  intellectual  occupation  is  the 
reception  of  impressions  from  the  senses  ;  and  by  the 
age  of  fourteen  years  the  powers  of  seeing,  hearing, 
tasting,  smelling,  and  feeling  are  in  their  fullest  per- 
fection. 

The  power  of  imagination  does  not  betray  any  ac- 
tivity until  the  child  is  more  than  a  year  old,  and  it  is 
later  in  attaining  its  full  vigor,  which  it  seldom  reaches 
before  the  age  of  twenty-one.  The  reasoning  power 
lies  half  dormant  still  later  than  the  imagination  ;  and 
seldom  shows  activity  till  after  the  seventh  year  ;  nor 
develops  its  full  strength  until  after  the  twenty-first. 
The  will  comes  to  its  maturity  of  power,  with  the  de- 
velopment of  reason. 

I* 


fO  TRUE    ORDER    OF    STUDIES. 

Nature  thus  indicates  that  a  teacher  in  educating 
a  child,  should  give  his  earliest  attention  to  the  devel- 
opment of  the  child's  perceptive  powers.  Moreover, 
among  these  powers,  those  of  external  sense  should  be 
the  first  to  receive  a  careful  training,  such  as  is  given 
in  the  admirable  Kindergarten  system  of  Froebel. 
Afterwards,  when  the  child  has  learned  to  perceive 
with  every  sense,  the  imagination  must  be  systemat- 
ically cultivated.  In  learning  to  observe,  he  will  learn 
to  remember  what  he  has  observed,  and  this  is  an  in- 
cidental culture  of  the  imagination  ;  but  he  must  also 
be  regularly  trained  to  invention.  This  is  admirably 
done  by  some  of  the  Kindergarten  gifts  ;  and  I  the 
more  cordially  express  my  approbation  of  the  treat- 
ment of  the  child  by  Froebel's  system,  because  I  dis- 
agree so  totally  with  him,  in  some  of  the  considera- 
tions by  which  he  would  explain  and  justify  his  treat- 
ment. 

Nature  further  indicates  that  a  child  should  not  be 
expected,  or  required  to  reason  at  an  early  age.  Any 
direct  training  of  the  logical  powers,  before  the  age  of 
twelve  years,  is  premature  ;  and,  in  most  cases,  a  posi- 
tive injury  to  the  scholar.  The  common  sense  view 
would  give  facts  before  reasoning.  Reasoning  upon 
the  facts  is  the  work  of  a  maturer  mind.  The  play  of 
the  imagination  should  from  the  beginning  be  com- 
pared with  or  contrasted  with  facts  ;  and,  in  the  later 
stages  of  education  be  carefully  guided  by  reason  and 
conscience. 


THE   HIERARCHY    OF   SCIENCES.  II 


CHAPTER  II. 

THE    HIERARCHY    OF  SCIENCES. 

IT  is  evident  that  we  cannot  teach  a  given  subject 
to  a  child,  before  he  is  old  enough  to  comprehend 
it,  nor  before  he  has  acquired  the  necessary  prelimin- 
ary knowledge.  In  order  to  learn  a  given  thing,  he 
must  be  sufficiently  mature,  and  sufficiently  well  in- 
formed. It  would,  for  example,  be  folly  to  attempt  to 
teach  a  boy  of  six  years  how  to  measure  heights  and 
distances,  by  a  theodolite  and  steel  tape  ;  or  to  teach  a 
boy  of  any  age,  who  was  ignorant  of  the  four  simple 
rules  in  arithmetic. 

It  is  the  object  of  the  present  chapter  to  inquire 
whether  there  is  any  comprehensive  order,  embracing 
all  the  objects  of  human  knowledge,  which  can  serve 
as  a  guide  in  the  selection  and  sequence  of  studies  ; 
that  is,  which  will  help  us  in  deciding  what  are  the 
proper  preliminary  studies  requisite  for  the  pursuit  of 
any  branch,  or  in  deciding  which  of  two  given  studies 
ought  to  be  placed  first  in  the  curriculum  of  a  school. 
If  the  discussion  should  appear,  to  any  reader,  dry  and 
abstract,  he  may  be  assured  it  will  be  brief  ;  and  that 
the  subsequent  chapters  shall  be  occupied  with  more 
practical  and  easily  intelligible  dctaibs. 

In  attempting  to  analyze  and   classify   the   great 


12  TRUE    ORDER    OF    STUDIES. 

field  of  human  knowledge,  we  obtain,  at  first,  a  separa- 
tion into  four  elements,  viz.  Space  and  Time,  Matter 
and  Spirit.  There  is  nothing,  existent  or  non-existent 
possible  or  impossible,  which  we  do  not  include  in  some 
sense,  under  one  of  these  four  heads  ;  while,  on  the 
other  hand,  there  is  no  one  of  these  four  which  we 
can  clearly  bring  under  another.  It  is  true  that  we 
might,  in  some  phases  of  mind,  be  tempted  to  consider 
Time  as  a  mere  abstract  notion,  formed  from  our  per- 
ception of  the  permafience  of  Space ;  it  is  true  that 
some  men  have  suspected,  from  the  marvellous  divers- 
ity of  the  powers  of  matter,  that  thought  is  but  a  mode 
of  motion  ;  it  is  also  true  that  the  obedience  of  Matter 
to  Spirit  leads  a  majority  of  men  to  believe  that  Mat- 
ter is  a  creation  of  Spirit  ;  but  these  opinions  are  not 
scientific  certainties,  like  the  existence  of  the  four 
elements. 

Of  these  four,  Space  and  Time  are  the  earliest  ob- 
jects of  distinct  intellectual  action.  The  attention  is 
called  to  them  by  the  phenomena  of  motion  and  the 
shapes  of  material  things.  The  forms,  and  motions  of 
things,  are  the  food  of  much  thought,  and  the  objects 
of  lively  attention  and  intellectual  action,  years  before 
the  other  myriad  problems  of  matter  begin  to  suggest 
themselves ;  still  longer  before  spiritual  character  and 
the  nature  of  the  mental  processes,  receive  any  atten- 
tion. It  is  true  that,  to  a  certain  degree,  all  these  ele- 
ments enter  into  some  of  the  earliest  states  of  con- 
sciousness ;  so  that  it  might  be  thought  that  the  knowl- 
edge of  them  is  gained  simultaneously.  But  they  are 
evolved  out  of  the  mist  of  the  child's  consciousness 


THE    HIERARCHY    OF    SCIENCES.  1 3 

one  by  one  ;  and  become  the  themes  of  distinct  men- 
tal efforts,  in  the  order  in  which  I  have  named  them. 
The  child's  knowledge  and  recognition  of  things  by 
their  shapes  long  precedes  any  definite  recognition  of 
time  or  rhythm  ;  and  becomes  varied  and  exact  to  a 
marvellous  degree,  while  as  yet  there  has  been  no  dis- 
tinct introversion  of  consciousness,  and  no  distinctly 
intellectual  appreciation  of  character. 

Whether  Spirit  created  Matter,  as  is  generally  be- 
lieved, or  not,  this  at  least  is  certain  ;  that  the  advanc- 
ing science  of  our  century  tends  rapidly  towards  prov- 
ing that  our  only  knowledge  of  Matter  is  gained  through 
its  being  the  realization  of  thought,  in  Space  and  Time. 
Sound,  color,  temperature,  and  other  sensible  proper- 
ties of  Matter,  are  revelations  to  us  of  modes  of 
motion  in  the  bodies  about  us.  It  is  probable  that 
without  motion  there  could  not  be  any  sensation  ;  cer- 
tainly the  human  imagination  tries  in  vain  to  imagine 
the  communication  of  sensation  without  motion.  But 
all  the  motions  thus  revealed  to  us,  through  our  sensa- 
tions, prove  on  examination  to  be  rhythmical  in  time, 
and  symmetrical  in  space.  The  body  which  by  its 
motion  reveals  its  existence  to  our  senses,  is  moving 
by  intelligible  law  ;  it  is  moving  in  consonance  with 
a  geometrical  and  algebraical  thought.  Thus  the 
sensible  properties  of  matter,  through  which  alone  the 
existence  of  matter  is  revealed  to  us,  reveal  to  us  di- 
rectly the  existence  of  thought,  anterior  to  the  present 
state  of  matter,  ruling  and  guiding  all  the  present 
manifestations  of  matter.  Thus  the  being  of  God  is 
manifest  through  the  existence  of  the  world  ;  and  the 


14  TRUE    ORDER    OF    STUDIES. 

world  can  be  apprehended  by  our  intellect,  even  in  its 
simple  sensible  properties,  only  because  those  proper- 
ties are  the  work  of  intellect.  And  this  creates  a 
strong  ^/rzm  probability  that  matter  is  an  absolute 
creation  ;  not  a  fashioning  of  original  material. 

We  awake  to  consciousness,  through  the  fact  of 
motion,  which  reveals  to  us  an  outer  world,  and  a  uni- 
verse of  Space  and  Time,  in  which  that  world  of  mat- 
ter moves.  These  space  and  time  relations  are  the 
earliest  objects  of  distinctly  conscious  intellection  ;  the 
first  objects  concerning  which  our  knowledge  takes  a 
scientific  form.  This  was  true  of  the  race,  and  it  is 
true  of  the  individual.  Before  the  child  has  a  clearly 
intellectual  life  on  any  other  subjects,  it  attains  a  very 
definite  power  to  distinguish  the  square,  the  circle,  the 
oval,  the  spiral  ;  to  recognize,  by  approximate  likeness 
of  outline,  even  rude  drawings  of  men,  dogs,  horses, 
cats,  cows,  trees,  and  various  articles  of  furniture  ;— 
and  also  to  recognize  the  rhythm  of  verse  and  music. 

Out  of  space  and  time  (which  have  by  some  wri- 
ters been  classed,  erroneously  as  I  think,  among  ab- 
stract notions,  as  though  mere  abstract  ideas  of  exten- 
sion and  duration)  arise,  through  the  suggestions  of 
the  material  world,  three  principal  sciences : — Geome- 
try, Arithmetic,  and  Algebra.  Geometry  deals  purely 
with  space,  and  considers  it  as  divided,  and  portions  of , 
it  as  bounded,  by  surfaces  ;  the  surfaces  divided  and 
bounded  by  lines  ;  the  lines  by  points.  Space  being 
in  itself  indivisible,  except  in  imagination,  we  are  led 
to  that  act  by  the  perception  that  matter  is  not  amor- 
phous ;  in  other  words,  we  are  led  to  imitate  the  act  of 


THE    HIERARCHY    OF    SCIENCES.  1 5 

the  Divine  Intellect,  which  has  geometrized  from 
eternity.  No  thoughts  enter,  indeed,  the  human 
mind,  except  at  the  suggestion,  reverently  followed,  or 
wickedly  perverted,  of  nature.  The  forms  of  material 
things,  conforming  to  the  Divine  Geometry,  suggest 
to  us  the  study  of  pure  forms  in  space,  and  thus  lead 
us  to  create  human  Geometry,  the  earliest  and  simplest 
of  all  possible  sciences. 

But  the  earliest  abstraction  from  the  idea  of  form 
is  that  of  number ;  and  out  of  this  idea  is  evolved  the 
earliest  of  the  truly  abstract  sciences,  namely  Arith- 
metic ;  which  thus  becomes  the  second  branch  in 
the  hierarchy. 

The  earliest  suggestions  of   motion  reveal  to    us 
time  as  well  as  space ;    and  although    these   two   ele- 
ments are  indissolubly  joined  in  every  phenomenon  of 
external  nature,  they  cannot  by  any  exertion    of  our 
intellect  be  made  to  appear  to  have  any  property  in 
common.     Space  is  external  to  the  mind ;  time  enters 
into  our  spiritual  consciousness,  and  measures  our  flow 
of   thought.     Sjoace  stands    immovable,  and    we   can 
move  our  bodies  through  it,  or  transfer  our  attention 
from  place  to  place  in  it,  at  our  own   will.      Time 
sweeps  past  us  with  irresistible  flow  ;  and  it  is  with  the 
greatest  difficulty  that  we  can  arrest   our  attention, 
even  for  a  few  moments,  upon  an  absolutely  instanta- 
neous epoch,  a  point  in  time.     Rhythmical  motion  con- 
nects, however,  the  abstract  idea  of  number  as  readily 
with  time  as  with  space  ;  and  time,  in  its   turn,   gives 
flexibility  to  the  idea  of   number,  connecting  it  more 
intimately  with  continuous  quantit)'  ;  from  which  con- 


l6  TRUE    ORDER    OF    STUDIES. 

nection  springs  the  third  science  ;  that  of  pure  Algebra. 
Out  of  these  three,  by  combination  and  development, 
have  sprung  the  wonderful  forms  of  the  Calculus, 
which  have  shed  such  lustre  upon  the  i/th  and  19th 
centuries. 

The  physical  properties  of  matter,  which  thus  sug- 
gested to  man  his  earliest  systematic  study  of  space 
and  time,  next  call  his  attention  to  matter  itself,  and 
the  laws  under  which  it  moves.  From  the  study 
of  motion,  recognized  as  such,  was  developed  the  sci- 
ence of  mechanics,  following  long  after  the  mathemat- 
ics, but  being  developed  with  greater  rapidity  after  it 
had  sprung  into  life.  Parts  of  this  general  science, 
such  as  acoustics,  and  optics,  were  not  recognized  at 
first  in  their  true  relation  to  motion,  and  held  there- 
fore, for  a  time,  an  apparently  independent  existence. 
Certain  of  the  phenomena  of  the  world,  which  modern 
science  declares  must  be  expressions  of  particular 
modes  of  motion,  suggest,  however,  the  idea  that  mat- 
ter exists  in  different  original  forms.  It  combines,  and 
separates,  into  apparently  new  substances  ;  and  the  laws 
by  which  it  thus  apparently  multiplies,  or  divides,  con- 
stitute chemistry.  Other  phenomena  in  nature  lead 
us  to  separate  certain  bodies  into  a  class  by  them 
selves  and  call  them  living.  They  are  to  all  appear- 
ance, not  under  the  strict  laws  of  mechanics  and  chem- 
istry, but  rather  use  those  law§  to  attain  their  indi- 
vidual ends;  each  growinginto  an  individual  form  of  spe- 
cific likeness  ;  growing,  not  by  a  mere  mechanical  aggre- 
gation of  particles,  nor  simply  by  a  chemical  separation 
of  kindred  particles,  but  growing  by  a  compound  pro- 


THE    HIERARCHY    OF    SCIENCES.  I7 

cess  of  chemical  analysis  and  synthesis,  and  mechanical 
building  according  to  a  complicated  intellectual  plan. 
The  study  of  matter  in  this  third,  most  exalted  stage 
of  its  action  is  Physiology  ;  which  completes  the  divi- 
sion of  Physics  ;  constituted  of  the  three  sciences. 
Mechanics,  Chemistry,  and  Physiology,  which  mani- 
festly stand  related  to  each  other  in  the  order  in  which 
I  have  named  them. 

Geometry  is  necessarily  the  first  study.  Arithmetic 
the  second,  Algebra  the  third  ;  as  I  have  defined  these 
studies,  they  must  be  understood,  in  some  degree  be- 
fore it  is  possible  to  understand  anything  further  ;  and 
the  three  physical  branches,  mechanics,  chemistry^ 
and  physiology  must  follow  in  that  order.  Many  per- 
sons may  be  unconscious  of  possessing  any  knowledge 
of  either  of  these  sciences,  except  arithmetic  ;  simply 
because  their  knowledge  has  not  been  acquired  from 
text  books,  and  is  not  arranged  in  their  minds  in  a  sys- 
tematic or  scientific  order.  Nevertheless,  any  skilful 
questioner  could  draw  out  of  them,  a  confession  of 
acquaintance  with  fundamental  facts  in  each  one 
of  these  six  branches  ;  and  thus  convince  them  that 
they  had  learned,  at  first  hand,  perhaps,  from  nature, 
many  valuable  truths  concerning  relations  of  space, 
time,  and  number  ;  mechanical  force,  chemical  changes, 
such  as  combustion,  oxidation,  fermentation,  and  de- 
cay ;  and  physiological  truths,  concerning  the  growth 
of  plants  and  animals,  their  food,  poisons,  sleep  and 
rest ;  and  these  have  been  acquired  in  their  due 
order  ;  the  knowledge  of  each  requiring  some  previ- 
ous knowledge  in  the  preliminary  branches. 


1 8  TRUE    ORDER    OF    STUDIES. 

The  more  extensive  physical  sciences  such  as  ge- 
ography, or  astronomy  may  be  considered  as  built  up 
of  the  simpler,  in  much  the  same  manner  as  the  wider 
mathematical  studies  are  a  combination  of  the  three 
elements  of  geometry,  arithmetic  and  algebra- 
After  acquiring  some  knowledge  of  material  things, 
the  pupil  naturally  turns  his  mind  towards  an  investi- 
gation of  the  uses  to  which  man  has  put  this  world  in 
which  he  has  been  placed.  The  attention  is  first 
caught  by  tools  and  machines,  fabrics  for  clothing, 
houses,  and  other  external  things  ;  by  the  mastery, 
one  might  say,  of  man  over  the  material  world  and  its 
subjection  to  the  uses  of  the  human  body.  Next  in 
order  the  child  observes  the  manner  in  which  man 
uses  matter  as  a  natural  vehicle  for  the  expression  of 
his  thought  and  feeling,  as  in  statues,  paintings  and 
music.  After  this  he  begins  to  give  consciously  his 
attention  to  the  wonderful  manner  in  which  men  ex- 
press thoughts,  by  conventional  modes  ;  which  may 
originally  have  been  but  abbreviations  of  more  natural 
expressions,  but  have  now  become,  like  the  clicking  of 
Morse's  telegraph,  merely  conventional  modes  of  ex- 
pressing propositions  of  the  intellect  or  emotions  of 
the  heart.  Finally,  among  the  actions  of  men,  he  rec- 
ognizes the  crowning  greatness  of  statesmanship,  of 
the  formation  of  States,  and  constitutions,  the  estab- 
lishment of  government  and  laws.  These  studies  I 
call  in  a  large  sense  of  the  word,  historical ;  and  con- 
sider them  as  coming  under  four  heads,  for  which 
there  are  no  thoroughly  satisfactory  names.  The  first 
head  embraces  manufactures,  commerce  and  agricul- 


THE   HIERARCHY   OF    SCIENCES.  1 9 

ture,  with  all  their  subsidiary  mechanic  arts.  The 
second  embraces  the  fine  arts, — the  third  deals  with 
language  and  literature  in  every  form.  The  fourth 
embraces  jurisprndence,  constitutional  law,  compara- 
tive legislation,  etc.  The  larger  sciences  created  by  the 
combination  of  these  heads  are  Political  Economy, 
Social  Statics  and  Dynamics,  and  History  in  its  or- 
dinary sense.  Thus  we  have  found  three  great  divi- 
sions of  the  hierarchy,  the  mathematical,  the  physical 
and  the  historical. 

But  when  the  child  is  mature  enough  so  to  do,  he 
begins  to  introvert  his  attention  upon  himself,  he  in- 
vestigates his  own  powers,  and  does  for  himself,  more 
or  less  correctly,  and  more  or  less  thoroughly,  what  I 
have  attempted  to  do  in  the  introductory  chapter  of 
this  book  ;  he  analyses  and  studies  the  powers  of  his 
own  soul,  and  developes  for  himself  an  intellectual 
philosophy,  a  doctrine  of  his  emotions,  and  a  code  of 
natural  ethics. 

Nor  can  he  stop  here, — he  inevitably  pushes  his 
thoughts  upwards,  and  enters  upon  theological  specu- 
lations. The  relation  of  the  Universe  to  its  Creator 
is  a  problem  that  no  man  of  any  intellectual  develop- 
ment can  put  aside.  Even  Herbert  Spencer,  who  has 
been  in  our  day  famous  for  the  strength  with  which 
he  has  maintained  that  we  can  assign  to  the  First 
Cause  of  the  Universe  no  attributes  whatever,  asserts 
with  equal  strength  and  emphasis  that  the  existence  of 
that  First  Cause  is  forced  constantly  on  our  attention, 
and  avouched  to  us  with  a  certainty  that  is  attained  by 
no  other  truth  whatever.     He  deprecates  theological 


20  TRUE    ORDER    OF    STUDIES. 

discussion  but,  nevertheless  regards  himself  as  taking 
the  most  preeminently  religious  view  of  the  origin  of 
things  ;  and  of  course  can  defend  this  claim  only  by 
theological  argument.  I  shall,  therefore,  continue  to 
count  Theology  as  the  head  of  the  Hierarchy  of 
Sciences. 

The  fivefold  division  at  which  we  have  thus 
arrived  may  be  set  forth  in  several  other  modes.  The 
mode  in  which  it  first  presented  itself  to  me  was  this  ; 
God  is  the  uncreated  Creator  ;  He  has  made  us  in 
His  own  image,  as  inferior,  created  creators  ;  we  have 
made  many  uses  of  this  world,  and  enacted  quite  a 
history  upon  it;  the  world  itself  is  deserving  of  our 
study,  independent  of  its  uses  to  us;  and  we  find  it 
can  exist,  and  manifest  itself  to  us,  only  as  it  floats  in 
space  and  endures  in  time.  This  gives  the  hierarchy 
in  its  descending  order;  but  in  education  we  need  its 
guidance  in  the  ascending  order.  In  that  order  it 
agrees  with  the  expanding  powers  of  the  child's  mind 
and  with  the  logical  sequence  and  dependence  of 
thoughts. 

We  can  form  dim  conceptions  of  the  spiritual 
attributes  of  the  Deity,  only  in  proportion  as  we 
understand  our  own  faculties,  in  which  lies  our  like- 
ness to  Him  ;  we  can  understand  the  human  faculties 
and  human  nature  only  as  we  observe  and  study  the 
words  and  deeds,  the  achievements  of  men  ;  we  can 
understand  the  achievements  of  man  only  as  we 
have  a  knowledge  of  the  theatre  wherein  he  has 
wrought,  and  the  material  he  has  had  to  work  upon  ; 
and  we  can  understand  this  heaven  and  earth,   only 


THE    HIERARCHY    OF    SCIENCES.  21 

in  proportion  to  the  clearness  and  profundity  of  our 
knowledge  of  the  laws  of  space  and  time  in  which 
they  exist. 

In  every  school,  therefore,  and  in  every  private 
tuition  of  a  child,  the  question  must  constantly  be 
asked,  not  only  whether  the  child  is  old  enough  to 
learn  what  you  are  attempting  to  teach  him,  but 
whether  he  has  the  requisite  knowledge  of  the  pre- 
liminary branches.  There  is  no  single  fact,  or 
doctrine,  in  Theology  or  in  Psychology,  which  does 
not  require  from  the  pupil,  some  definite  preparation 
in  historical,  physical  and  even  mathematical  studies. 
What  that  preparation  ought  to  be,  is  an  important 
question  ;  and,  in  seeking  an  answer,  the  Hierarchy 
of  Science  is  a  valuable  guide.  The  scheme,  carried 
more  into  detail,  will  be  found  in  the  following  table. 


22 


TRUE    ORDER    OF    STUDIES. 


THEOLOGY, 


The  Infinite 

Spirit, 

the 


Seligion, 


Natural  Theo- 

Unlimited  Will;  logy, 


PSYCHOLOGY,  |  the 


„  Ethics, 

«-i    The  Finite  Spirit,  .= 

a  Esthetics, 


S     Limited  Will ;    ^  Mental  Philo- 
*S  o      sophy, 


SCIENCE,    I      HISTOEY, 


The  Acts  of  Man, 

the 

Creations  of  the 

Finite  Will ; 


■g  Law, 

•3 

•^  Language, 

E 

S  Art, 

cT 

^  Trades 


NATUEAL 
HISTOEY, 


The  Material 

Worid, 

the 

Creations  of  the 

Infinite  Will ; 


I  Biology, 
■^  Chemistry, 
Z  Mechanics, 


MATHEMA- 
TICS, 


or,  The 

Field  of  Time 

and  Space 

in  which  Creation 

is  wrought ; 


Algebra, 

Arithmetic, 

Geometry, 


THE   HIERARCHY   OF    SCIENCES. 


23 


The  Relations  of  God  to 
the  Human  Soul  and 
to  Finite  Spirits, 


His    Relations     to     the 
World  and  to  History. 


Investigation  of  particular 
Fields  of  Religious  In- 
quiry, 


Investigation  of  particular 
Fields  in  Natural  The- 
ology, 


Evidences  of  Chris- 
tianity, 

Dogmatic  Theology, 


The  Will  and  the   Ideas    c 
of  Duty,  &c.,  £ 

The  Emotions  and  Ideas  ."« 
of  Beauty,  &c.,  ^ 

p. 

The   Mind  and   Ideas  of    „ 
Truth,  &c., 


Discussions  of  particular 
Relations  in  an  Etliical 
Light, 

Analysis  of  particular 
Classes  of  Emotions, 

Metaphysics, 
Logic, 


Theory  of  Education* 


The  Attempts  of  Man  to 
enforce  his  Ideas  on  his 

>    Law  of  Nations, 
'Si  Constitutional  Law. 

3 

Fellows. 

c    Jurisprudence, 
.2    Philology, 

.C 

History, 

The   Use  of  Symbols  to 

•53    Rhetoric, 

E 

express  Ideas. 

c.  Poetry, 

m 

The   Material   World   as 
naturally   expressive  of 
Thought  and  Feeling. 

S    Music, 
S    Painting, 
j^    Sculpture, 
_    Architecture, 

c 

Social  Science, 

The    Matenal   World  m 

.2    Commerce, 

Political  Economy, 

Material  Uses. 

|3    Manufactures, 

>. 

A<    Agriculture, 

E 

Zoology, 
Botany, 
Physiology, 
Organic  Chemistry, 
Inorganic  Chemistry, 
Electrics, 
Themiotics, 
Matter  as  the  subject  of  Q    Optics, 
Mouons.  >>  Acoustics, 

-"    Dynamics, 
£  Statics, 


Plants  and  Animals,    or 
Matter  as  living. 

Matter   as    distinguished 
into  Kinds. 


o    Geology, 


Geography, 


Astronomy, 


Tlie   Ideas    of    Time    or  ^  theory  of  Functions, 

Progression.  ^  Theory  of  Equations, 

H  Theory  of  Probabilities, 

Number  and  Ratio.  Theory  of  Numbers, 

Analytical  Geometry, 
Space,  Distance,  and  Di-         Trigonometry, 
rection.  Descriptive  Geometry, 

Plane  and  Solid  Geometry 


Kinematics, 
The  Calculus, 


Quaternions, 
Stigmatics. 


24  TRUE    ORDER    OF    STUDIEiJ. 


CHAPTER  III. 

MATHEMATICS. GEOMETRY. 

WE  have  endeavored,  in  the  preceding  chap- 
ter, to  show,  that  all  possible  objects  of 
human  thought  are  comprised  under  one  or  another  of 
these  five  heads :  Mathematics,  Physics,  History, 
Psychology  and  Theology.  In  making  these  the  objects 
of  study,  mathematics  must  precede  physics,  because 
conceptions  of  form,  time  and  number  must  precede 
conceptions  of  material  phenomena.  For  example ,  me- 
chanics treats  of  motion,  in  straight  or  curved  lines, 
of  the  parallelogram  of  forces,  and  direction  of  reflect- 
ed and  refracted  motion,  of  the  strength  of  materials 
as  dependent  on  form,  of  the  equilibrium  of  the  arch  ; 
and  in  these  and  other  problems,  demands  a  prelimin- 
ary knowledge  of  geometry.  Chemistry  deals  with 
definite  proportions,  atomic  weights,  permutations  of 
combinations,  multiples  in  scries,  and  other  matters, 
necessarily  involving  a  preliminary  knowledge  of 
arithmetic.  Botany  and  zoology  in  their  morphology 
require  geometry  ;  in  their  physiology,  chemistry  ;  in 
both  departments,  mechanics. 

As  mathematics  thus  necessarily  precede  physics, 
so  physics  must  precede  history.     All  that   men  do  in 


MATHEMATICS. GEOMETRV.  2$ 

this  world,  must  be  done  upon  the  materials  set  before 
us,  and  under  the  conditions  imposed  by  physical 
laws.  Our  thoughts  can  find  expression  only  through 
ouiward  symbols,  in  things  built  or  made,  in  imitative 
arts,  or  in  language ;  which,  when  verbal,  was  all 
originally  figurative,  and  when  musical,  is  subject  to 
laws  of  rhythm  and  elasticity.  The  history  of  human 
thought  must  also  include,  as  one  of  its  most  import- 
ant chapters,  the  history  of  the  physical  sciences,  and 
thus  demand  some  knowledge  of  those  sciences. 

Moreover,  Psychology  can  be  advantageously 
studied,  only  by  one  acquainted  to  some  extent  with 
physiology,  and  with  history.  ■  We  know  nothing  of 
the  powers  of  the  soul,  except  as  we  manifest  them,  or 
see  them  manifested  by  others  ;  and  in  judging  of  the 
soul  from  our  external  action  as  interpreted  by  con- 
sciousness, we  must  also  learn  what  allowance  to 
make  for  the  automatic  action,  under  physiological 
laws,  of  the  body  in  which  we  dwell. 

Lastly,  we  have  endeavored  to  show  that  Theology 
requires  a  knowledge  of  all  the  inferior  branches. 
We  can  know,  by  nature,  nothing  concerning  the 
Creator,  in  whose  image  we  were  made,  except  by 
studying  his  works,  and  especially  by  studying  that 
image  of  Himself  which  He  has  placed  within  us. 
We  may  have  religion  with  very  Httlc  theology  ;  but 
we  cannot  have  any  theology  at  all  without  some 
previous  knowledge  of  the  lower  branches,  and  espe- 
cially of  psychology. 

Thus  it  is  evident  that  the  mathematics  take 
logical  precedence,  as  the  great  and  indispensable  f  oun- 


26  TRUE    ORDER    OF    STUDIES 

dation  of  all  learning.  It  is  not  only  impossible  to  dis- 
pense with  them,  but  impossible  to  place  them  any- 
where else  than  at  the  beginning  of  all  intellectual 
education.  All  intellectual  life  upon  our  planet  begins 
with  geometry ;  it  was  so  with  the  race  ;  it  is  so  with 
the  individual.  A  man's  geometrical  knowledge  may 
have  been  learned  unconsciously,  as  M.  Jourdain's 
prose  ;  but  it  is  no  less  a  real  knowledge  of  space  and 
form,  and  no  less  the  real  foundation  for  all  the  other 
knowledge  he  possesses  ;  first,  for  his  knowledge  of 
number,  of  rhythm,  of  time  ;  then  for  his  knowledge  of 
business,  morals,  politics,  and  religion. 

A  natural  method  of  education  requires  us,  there- 
fore, to  pay  our  earliest  attention  to  the  development 
of  the  child's  power  to  grasp  the  truths  of  space  and 
time,  his  mathematical  power. 

The  three  great  branches  of  the  mathematics  are 
Geometry,  Arithmetic  and  Algebra.  If  the  reason 
for  arranging  them  in  this  particular  order  is  not  clearly 
apparent,  on  a  consideration  of  the  sciences  them- 
selves, it  may  become  clearer  on  considering  the 
sequence  in  the  development  of  the  child's  power  of 
thought.  Number,  although  an  abstraction  very 
early  made  from  the  contemplation  of  forms  in  space 
is  manifestly  subsequent  to  the  perception  of  the 
forms  themselves.  The  child  recognizes  hundreds 
of  objects  from  their  shapes  long  before  he  could  be 
taught  to  count  them ;  therefore,  geometry  precedes 
arithmetic  in  education.  Again,  time  is  much  more 
difficult  to  see,  than  space ;  it  requires  a  riper  effort  of 
the  imagination  to  separate  time  from  the  succession 


MATHEMATICS. GEOMETRY.  2/ 

of  events,  than  to  separate  space  from  the  extension 
of  bodies.  Space  remains,  so  to  speak,  visible,  to  the 
mental  eye  ;  but  time  cannot,  by  any  device  of  the 
imagination,  be  made  to  appeal  to  sense.  Algebra, 
therefore,  the  science  of  time,  follows  arithmetic,  as 
arithmetic  follows  geometry.  Every  day,  from  the 
hour  of  birth,  a  new  knowledge  of  forms  developcs 
new  power  in  numbers  ;  and  that  again,  new  power  in 
the  consideration  of  flowing  or  changing  quantity  ; 
and  thus  the  child  runs  its  round ;  from  geometry  to 
Theology,  and  then  to  a  higher  point  in  geometry,  and 
round  again  to  Theology  ;  in  ever  recurring  five-fold 
cycles,  as  long  as  it  continues  its  intellectual  develop- 
ment and  growth. 

Until  the  age  of  four  or  five  years,  the  child  is 
seldom  at  school,  and  seldom  directed  at  all  with  a 
view  to  intellectual  education.  The  best  parents, 
usually,  content  themselves  with  looking  after  its 
physical  health,  and  its  habits  of  obedience  and  order 
in  the  house.  Nevertheless  the  education  of  the  first 
years  of  life  is,  in  many  respects,  more  important 
than  any  which  follows.  There  can  be  no  doubt  that 
early  impressions  are  very  deep,  and  exert  great  power 
over  the  subsequent  life,  physical,  intellectual  and 
moral.  Every  observer  knows  the  difficulty  of  cor- 
recting the  moral  habits  of  a  spoiled  child.  The 
difficulty  of  correcting  his  intellectual  habits,  although 
less  apparent,  is  as  real.  For  this  reason,  I  have 
endeavored  to  persuade  the  school  committees  with 
which  I  have  been  connected,  to  secure  the  highest 
talent  and  pay  the  highest  wages  in   the  schools  for 


28  TRUE    ORDER    OF    STUDIES. 

the  youngest  pupils  ;  convinced  that  this  would  in  the 
end,  most  truly  elevate  the  character  of  the  whole 
community. 

For  the  geometrical  education  of  children  under 
five  years  of  age,  the  early  kindergarten  gifts  are 
admirably  adapted.  Picture  books,  provided  the 
drawing  is  good,  are  also  valuable  ;  and  many  of  the 
toys  given  to  children  serve  a  good  purpose  in  this 
direction. 

We  must,  however,  remember  that  the  great  ends 
to  secure,  by  early  geometrical  culture,  are  accuracy 
of  observation,  and  definiteness  of  imagination.  These 
uses  of  geometry  have  been  strangely  neglected  by 
both  friends  and  foes  of  this  intellectual  gymnastic. 
The  admirers  of  geometry  have  contended  themselv^es 
with  showing  that  no  other  study  holds  the  student  to 
such  continuity  of  thought,  to  such  extended  series  of 
consecutive,  dependent  arguments.  And  in  Sir 
William  Hamilton's  plea  against  the  use  of  geometry 
in  education,  he  contents  himself  with  showing,  as  he 
thinks,  that  other  sciences  afford  better  training  for 
the  powers  of  logical  thought. 

But  the  powers  of  perception,  and  the  powers  of 
imagination,  or  conception,  are  of  even  greater 
importance  than  those  of  reasoning  ;  they  give  us  the 
facts  of  nature,  and  definite  theorems  in  science, 
without  which  reasoning  is  vague  and  worthless.  The 
early  studies  of  the  child,  therefore,  while  seeking  to 
develope  his  ideas  of  space,  and  time,  must  do  so  by 
training  him  to  rapid  and  exact  observation,  clear  and 
definite  conception. 


MATHEMATICS. GEOMETRY.  29 

Miss  Edgeworth,  in  one  of  her  invaluable  stories, 
describes  small  wooden  bricks  ;  rectangular  parallelo- 
pipcds,  whose  dimensions  are  in  the  ratio  1:2:4.  I" 
the  public  schools  of  Waltham,  we  used  to  supply  the 
scholars,  under  lO  years  old,  with  such  bricks,  made 
of  birch  or  maple,  two  inches  long,  one  inch  wide> 
half  an  inch  thick  ;  with  a  small  percentage  of  double 
length,  and  half  length.  Each  scholar,  when  playing 
with  these  bricks  in  school,  had  his  desk  covered  with 
a  piece  of  dark  cotton  velvet,  to  prevent  noise,  and 
prevent  slipping.  For  younger  children  before  they 
come  to  school  the  bricks  may  be  larger,  and  of  lighter 
wood.  A  child  of  eighteen  months  old  will  find  amuse- 
ment in  them.  The  variety  of  structures,  all  beautiful 
and  symmetrical,  which  an  ingenious  boy,  of  ten  years, 
will  make  with  a  few  dozen  of  such  bricks,  would 
astonish  the  unitiated.  Square  and  circular  build- 
ings, pyramids,  crosses,  gateways,  columns  surmount- 
ed by  crosses,  and  natural  arches  of  various  forms, 
will  be  devised  by  the  child,  and  combined  in  a  variety 
of  modes.  For  the  building  of  real  arches,  centerings 
must  be  provided,  and  also  a  substitute  for  mortar  in 
the  shape  of  numerous  little  sticks,  like  Vienna  matches 
without  phosphorus,  one  to  be  inserted  in  each  joint 
of  the  arch,  before  the  centring  is  removed.  This 
process,  as  well  as  the  breaking  of  joints,  binding  of 
crosses  together,  erecting  of  the  long  cross-bar  in 
crosses,  etc.,  will  give  incidental  instruction  in 
mechanics,  as  well  as  in  geometry.  It  will  also  give 
valuable  lessons  on  the  importance  of  precision,  and 
promptness  in  action  and  observation. 


30  TRUE    ORDER    OF    STUDIES. 

The  Chinese  tangram  consists  of  seven  pieces  of 
flat  metal  or  wood  : — five  isosceles  right  triangles,  a 
rhomboid  and  a  square.  The  area  of  the  seven  pieces 
being  called  unity,  the  areas  of  the  square,  the 
rhomboid,  and  one  of  the  triangles,  are  each  one- 
eighth  ;  two  of  the  remaining  triangles  one-sixteenth 
each  ;  and  the  other  two  one-quarter  each.  They  are 
accompanied  by  a  book  containing  hundreds  of  oddly 
shaped  rectilinear  figures  ;  any  one  of  which  may  be 
made  by  putting  all  the  seven  pieces  together. 
Learning  that  Archimedes  had  invented  a  similar 
game,  and  ascribed  to  it  an  educational  value  ;  but 
feeling  that  the  Chinese  tangram  was  too  difficult  for 
beginners,  I  published  in  1848  a  much  simpler  form 
and  introduced  it  into  the  schools  of  Waltham,  where 
it  was  used  for  many  years.  Two  hundred  and  four 
figures  were  given,  each  capable  of  analysis  into  three 
isosceles  right  triangles ;  and  the  area  of  these 
triangles  were  either  the  ratio  i  :  i  or  i  :  2.  These 
"  puzzles  to  teach  geometry,"  cultivate  the  habit  of 
exact  observation,  and  of  the  rapid  analysis  of  forms. 
They  may  also  be  made  of  curvilinear  figures.  I 
have  frequently  used,  instead  of  triangles,  trigonoid 
figures,  each  being  enclosed  in  three  arcs,  one  of  120°, 
and  two  of  60°.  Two  varieties  of  the  trigonoid  are 
procured  by  having,  in  some,  both  arcs  of  60°  con- 
cave, in  other  only  one. 

At  the  earliest  stage  of  schooling  the  child  may 
be  taught  also  to  derive  instruction  from  his  slate  and 
pencil.  Agassiz  is  reported  to  have  said,  in  regard  to 
observation  in  Natural  History,  that  a  lead  pencil  is  a 


CTATE  NORIV; 

Los  Angelfc^i,  '^i\\. 

MATHEMATICS. GEOMETRY.  3  1 

very  good  microscope  ;  and  the  slate  pencil  serves  the 
same  purpose  for  the  younger  pupil,  in  the  more 
fundamental  study,  of  geometrical  forms.  When  the 
child  can  use  the  pencil,  he  can  also  use  the  crayon 
upon  the  blackboard  ;  and  the  ingenuity  and  skill  of 
men  in  Waltham,  have  brought  white  crayons  of  the 
best  quality  within  the  reach  of  every  school.  As  a 
suggestion  of  the  mode  in  which  the  pencil  and 
crayon  may  be  made  to  conduce,  rapidly,  to  accuracy 
and  quickness  in  the  perception  of  geometric  form, 
take  the  following  exercise. 

Let  the  teacher  have  cards  or  tablets  each  con- 
taining one  clearly  drawn  simple  figure.  For  younger 
classes  these  figures  may  be  ;  a  horizontal  straight 
line,  a  vertical  line,  a  line  slanting  to  the  right,  a  line 
slanting  to  the  left,  a  St.  George's  cross,  a  St. 
Andrew's  cross,  an  arrow  head,  an  arc  in  one  position 
or  another,  etc.  For  classes  a  little  older  the  figures 
may  be  triangles  in  different  forms  and  positions^ 
circles,  circles  with  a  diameter  in  different  positions, 
ellipses  of  different  forms  and  positions,  capital 
letters,  etc.  Classes  still  more  advanced  may  take 
lower  case  letters,  Roman  and  Italic,  outlines  of 
forest  leaves,  profiles,  outlines  of  familiar  animals, 
utensils,  etc.,  Gothic  arches,  numerals,  etc.  These 
cards,  or  tablets  may  be  permanently  printed,  or  they 
may  be  made  extempore  by  the  teacher,  a  slate  with  a 
crayon  drawing  will  answer  every  purpose,  in  the 
hands  of  a  teacher  who  can  draw  rapidly  and  correctly. 
The  class  being  ready  with  their  slates,  or  at  the 
blackboard,  the  teacher  calls  their  attention,  and  ex- 


32  TRUE    ORDER    OF    STUDIES. 

poses  her  card  for  a  few  seconds,  longer  to  absolute 
beginners  in  the  exercise,  but  afterwards  for  still 
shorter  times,  until  it  is  reduced  to  a  minimum  ex- 
posure. Then  each  pupil  draws  immediately  from 
memory  a  reproduction  of  what  was  shown,  and  ex- 
hibits it  for  criticism.  This  will  be  found  an  admir- 
able preparation  for  subsequent  observation  of  objects 
of  natural  history. 

When  the  child  is  able  to  analyze  figures  com- 
posed of  three  or  four  triangles  ;  and  to  copy  triangles 
and  rectangles  with  approximate  similarity  to  his  copy, 
he  will  be  ready  for  conversations  upon  geometrical 
theorems.  The  steady  aim  of  the  teacher  in  these  con- 
versations must  be  to  lead  the  child  to  see  for  himself; 
not  to  learn  words  by  rote ;  much  less  to  learn  reasons 
for  belief;  but  to  see  the  truth,  directly,  without  the 
intervention  of  reasoning,  and  without  appeal  to  rea- 
soning for  verification.  Whatever  proposition  you  an- 
nounce to  him,  announce  to  him  as  known,  and  to  be 
received  by  him,  for  the  present,  simply  as  food  for  his 
imagination  ;  do  not  attempt,  nor  lead  him  to  attempt 
to  prove  it,  nor  to  use  it  as  proof  ;  that  exercise  of 
logic  belongs  to  a  later  period  in  his  course.  If  the 
child  asks  for  proof,  and  the  demonstration  is  fully 
within  the  grasp  of  his  mind,  it  may  do  no  harm  to 
give  it  ; — but  it  will  be  an  exceptional  case  ;  there  are 
very  few  children  under  twelve  years  of  age,  capable 
of  understanding  the  simplest  geometrical  demonstra- 
tion. On  the  other  hand  I  have  seen  scores  of  child- 
ren in  the  primary  schools  of  Waltham,  under  ten 
years  of  age,  who  by  familiar  oral  instruction  on  the 


MATHEMATICS. GEOMETRY.  33 

part  of  the  teacher,  had  been  made  well  acquainted 
with  the  leading  truths  of  the  geometry  of  the  trian- 
gle and  the  circle  ;  many  also  under  twelve  years,  who 
had  in  like  manner  attained  a  clear  knowledge  of  the 
relations  of  the  cycloidal  curves,  and  their  evolutes ; 
and  of  many  theorems  concerning  the  conic  sections 
and  the  catenary  curve. 

The  ease  of  imparting  such  information,  or  lead- 
ing the  child's  imagination  into  such  exercises  is  greater 
than  the  teacher  who  has  not  tried  it  would  imagine. 
Take  any  clear-headed  boy  of  ten  or  twelve,  and  sup- 
pose to  him  the  case  of  a  goat  on  a  plain,  tethered 
to  a  ring,  sliding  on  a  cord,  fastened  at  either  end  to 
one  of  two  stakes,  whose  distance  apart  is  less  than 
the  length  of  the  cord.  Question  him  about  the  goat's 
liberty  of  movement,  and  you  will  very  readily  lead 
him,  by  questions  only,  to  see  that  the  ring  is  confined 
to  an  oval,  which  is  symmetrical  on  two  rectangular 
axes  (he  of  course  will  not  use  these  technical  phrases  of 
words  but  he  will  describe  the  facts),  the  longer  diam- 
eter passing  through  the  stakes,  and  that  the  sum  of 
the  distances  from  any  point  in  the  periphery  to  the 
two  stakes  will  be  constant,  and  equal  to  the  longest 
diameter.  Then  imagine  a  dove  for  the  goat,  a  finger 
ring  and  thread  tied  to  the  tops  of  two  tall  poles  and 
you  can  lead  him  to  discern  the  form  and  some  of  the 
properties  of  the  prolate  ellipsoid. 

Now  if  it  be  asked  ot  what  value  are  these  geo- 
metrical conceptions  to  the  scholars  who  have  thus 
early  attained  to  them,  I  answer  that  the  uses  of  the 
knowledge  will  be  manifold.     It  has  already  afforded 


34  TRUE    ORDER    OF    STUDIES. 

to  each  of  them  an  excellent  culture  in  the  power  of 
clear  and  definite  conception  ;  it  has  enlarged  their 
sphere  of  thought,  and  linked  the  higher  mathematical 
truths  with  their  playthings, —  the  hoop,  the  swing,  the 
jumping  rope,  the  ball,  and  its  movements  ;  it  has 
made  them  partakers  in  the  fruit  gathered  by  the 
highest  spirits  of  our  race. 

The  clearness  and  precision  of  observation  and 
imagination,  cultivated  by  these  early  geometrical 
studies,  will  be  of  use  in  every  occupation  of  life  ; 
and  render  the  student's  testimony  and  his  judgment 
of  more  value  in  after  life,  both  to  himself  and  to 
other  men.  Even  the  powers  of  the  eye  and  of  the 
hand  will  be  more  likely  to  be  cultivated  with  care, 
for  uses  of  industrial  art,  by  one  whose  imagination 
has  been  thus  developed  and  strengthened.  And  if 
there  chance  to  be,  among  the  children  thus  early  im- 
bued with  the  germs  of  geometry,  any  scholar  whose 
natural  gifts  peculiarly  fit  him  to  advance  its  progress, 
or  to  use  the  higher  mathematics  to  advantage,  noth- 
ing could  more  surely  lead  him  to  application,  and  im- 
provement of  his  gifts,  than  to  set  before  him  at  an 
early  age  some  of  the  curious  and  interesting  results 
that  have  been  attained  by  the  labor  of  his  predeces- 
sors. As  the  visible  forms  of  nature  stimulate  the 
imagination,  so  the  creations  of  the  imagination  stimu- 
late the  reason. 

The  sight  of  a  hanging  chain,  for  example,  may 
stimulate  the  imagination  to  conceive  of  a  chain 
formed  of  infinitesimal  links,  producing  a  uniform 
curve.     This  conception  arouses  the  logical  powers  to 


MATHEMATICS. GEOMETRY.  35 

inquire  into  the  relations  of  the  parts  of  such  curve 
tf>  each  other,  and  to  the  forces  which  hold  it  in  equi- 
librium. A  boy  of  ten  years  old  playing  with  such  a 
cliain,  may  readily  learn  some  of  the  truths  which 
such  inquiries  bring  to  light.  He  may  roughly  test  by 
his  muscular  exertion,  or  more  accurately  test  by  a  lit- 
tle mechanical  ingenuity  and  measurement,  the  truth 
of  your  assertion,  that  the  length  of  a  piece,  of  the 
same  chain,  equal  in  weight  to  the  horizontal  tension, 
will  strike,  used  as  radius,  a  circle  just  large  enough  to 
fit  exactly  the  lower  part  of  the  chain  ;  and  may  easily 
be  led  to  draw  the  corollary  that  no  amount  of 
power  can  draw  a  horizontal  flexible  thread  perfectly 
straight.  The  marvcllousness  of  this  corollary  will 
fix  the  theories  ineradicably  in  his  memory,  and  he 
will,  years  afterward,  when  he  begins  to  learn  how  to 
demonstrate  the  theories  of  geometry,  wish  to  prove 
the  proposition.  But  he  finds  that  simple  geometry 
is  not  enough.  He  takes  up  algebra,  learns  to  apply 
it  to  geometry  ;  but  the  problem  is  still  too  difficult  for 
him  ;  he  adds  the  resources  of  trigonometry,  but  is 
no  nearer  the  proof  that  he  desires.  He  enters  col- 
lege, learns  the  marvellous  uses  of  Descartes'  coordi- 
nates ;  but  finds  his  chain  still  hangs  beyond  the 
reach  of  their  magic.  Nor  is  his  curiosity,  aroused  at 
so  early  an  age,  gratified  until,  perhaps  in  his  senior 
year,  having  learned  something  of  the  wonderful  cal- 
culus of  Leibnitz  and  Newton,  something  of  the  an- 
alytical mechanics  of  Lagrange,  he  takes  up  the  discus- 
sion of  the  catenary  curve. 

The  student  who  has  in  childhood  become  familiar 


36  TRUE    ORDER    OF    STUDIES. 

with  the  facts  of  geometry,  approaches,  when  nearer 
manhood,  higher  mathematical  studies  under  less  dis- 
advantage than  others.  The  student  who  betakes  him- 
self, as  preparatory  to  higher  engineering  or  architec- 
ture, to  the  study  of  the  conic  sections,  the  arch  of 
equilibrium,  and  other  transcendental  curves,  has  usu- 
ally a  twofold  difficulty  ;  he  is  receiving  novel  and  be- 
wildering ideas,  at  the  very  time  that  he  is  also  learn- 
ing a  new  language  in  which  to  express  them.  But  if 
he  has  already  become  familiar  with  the  properties  of 
the  curve,  and  easily  form  a  clear  picture  of  it  in  his 
imagination,  he  can  give  his  whole  attention  and  whole 
strength  to  the  mastery  of  the  language,  the  analytical 
key  that  unlocks  the  hidden  treasure-houses  of  the 
Science  of  Space. 

In  order  to  facilitate  the  formation  of  habits  of 
precise  imagination  at  the  beginning  of  the  course,  we 
introduced  into  the  Waltham  Schools,  to  be  used  upon 
the  teacher's  desk,  several  pieces  of  home-made  aj> 
paratus,  for  the  mechanical  production  of  curves  and 
illustrations  of  theorems. 

When  he  attains  the  age  of  12  or  13  years,  the 
pupil  having  learned  a  little  arithmetic  also,  may  be- 
gin problems  of  geometrical  construction.  I  have 
known  boys,  at  that  age,  who  made  quadrants,  and 
horizontal  circles  for  themselves,  and  solved  graphic- 
ally, problems  in  heights  and  distances,  and  surveying  ; 
and  who  habitually  carried  in  their  breast  pockets,  sun- 
dials of  their  own  construction,  which  by  a  thread 
and  plumbline,  gave  them  the  hour  of  the  day. 

A  year  or  so  later,  the  pupil  will  be  mature  enough 


MATHEMATICS. GEOMETRY.  37 

to  comprehend  geometrical  reasoning.  The  ordinary 
text-books  on  geometry  fail,  as  I  think,  in  their  adap- 
tation to  children  from  three  circumstances.  First, 
in  not  explaining  the  object  of  reasoning.  The  child 
plunges  into  demonstrations,  without  having  any  con- 
ception of  what  demonstration  is,  or  what  it  proposes 
to  do  ;  and  he  not  unfrequently  passes  through  his 
whole  course  of  mathematical  instruction  in  a  state  of 
bewilderment,  never  having  clearly  perceived  the 
force  of  a  Q.  E.  D.  Secondly,  the  ordinary  text-books 
give  their  propositions  in  a  disconnected  manner,  so 
that  it  is  only  by  accident  that  some  scholar,  brighter 
than  the  average,  perceives  that  to  attain  to  some  of 
his  propositions  in  isoperimetry  he  must  weave  a  con- 
nected series  of  two  or  three  hundred  propositions, 
not  one  of  which  can  be  omitted,  or  transposed,  with- 
out destroying  the  validity  of  the  whole  argument. 
Thus  geometry  loses  much  of  the  very  excellence  for 
which  it  is  commonly  extolled,  the  teaching  of  a  pa- 
tient continuity  of  attention,  of  a  close  adherence  to 
the  logical  sequence  of  thought.  Thirdly,  the  usual 
treatises  confine  themselves  to  the  demonstration  of 
theorems  and  solution  of  problems;  —  giving  no  ex 
ercises  to  be  solved  by  the  pupil,  as  in  arithmetic  and 
algebra,  and  in  various  arts  of  mensuration.  In  my 
"  Second  Book  in  Geometry  "  I  endeavored  to  reme- 
dy these  three  defects,  by  explaining  carefully,  in  pre- 
liminary chapters,  the  object  of  demonstration  ;  by 
giving  demonstrations  of  only  two  theorems,  but 
selecting  such  as  required  the  demonstration  of  about 
two   hundred   preliminary    propositions ;  and   by  ap- 


38  TRUE    ORDER    OF    STUDIES. 

pending  unsolved  theorems  and  problems  to  some  of 
the  chapters.  I  have  been  partially  followed  in  the 
second  and  third  of  these  reforms,  by  William  F. 
Bradbury,  and  hope  that  other  writers  on  the  subject 
will  be  led  into  the  same  path. 


ARITHMETIC.  39 


CHAPTER  IV 

ARITHMETIC. 

AT  the  same  time  that  the  child  is  expanding  his 
powers  of  geometrical  conception, — let  us  say 
from  the  age  of  five  or  seven,  to  that  of  eleven  or 
twelve,  according  to  his  natural  ability, — he  should 
also  be  gaining  simple  ideas  of  numbers.  Before  he 
enters  school  he  has  usually  gained,  without  effort  or 
intention  on  the  part  of  his  parents,  sufficient  knowl- 
edge of  shapes  and  forms,  to  serve  as  the  basis  of  a 
partial  knowledge  of  numbers  under  five.  Let  his 
schooling  in  arithmetic  begin  with  developing,  and 
making  clear,  these  partial  and  confused  ideas.  The 
order  of  nature  requires  that  this  should  be  done  at 
first  by  concrete  illustrations  ;  beans,  grains  of  corn 
marbles,  pencils,  buttons,  blocks,  or  counters.  Ou 
the  whole  beans  are,  when  we  wish  to  illustrate  large 
numbers,  the  best  ;  being  at  once  cheap  and  clean. 

The  method  of  teaching  which  has  always  seemed 
to  me  the  most  natural  and  effective,  is  substantially 
that  which  has  recently  been  called  Grube's  method  ; 
but  which  has  probably  suggested  itself,  independ- 
ently, to  many  thoughtful  educators.  A  number  is 
the  answer  to  the  question  how  many  ;    but  the  usual 


40  TRUE    ORDER    OF    STUDIES. 

method  of  teaching  a  child  to  count  is  apt  to  produce 
a  confusion  in  its  mind  between  ordinal  place  and 
numbers.  Counting,  or  naming  numbers  in  their 
order,  should  not  be  taught  until  the  child  has  learned 
to  recognize  the  numbers  themselves.  Expose  suc- 
cessively, in  front  of  a  little  book  or  slate,  the  fore- 
finger, little  finger,  ring  finger,  middle  finger  ; — asking 
each  time,  "  How  many  fingers  do  I  show,"  and 
dictating,  if  the  child  cannot  answer,  the  answer,  one. 
In  like  manner,  show  successively  fore  and  middle, 
fore  and  ring,  fore  and  little,  middle  and  ring,  middle 
and  little,  ring  and  little  ;  asking  at  each  exhibition, 
the  same  question,  and  dictating,  if  the  child  hesitates, 
the  answer,  two.  Exhibit  in  like  manner,  first  one, 
and  then  two,  beans,  pencils,  marbles,  books,  chalk 
marks,  chalk  crosses,  letters  of  the  alphabet,  etc., 
varying  the  position  and  direction  of  the  couples,  until 
you  are  assured  that  the  child  really  knows  the  mean- 
ing of  the  words,  two,  and  one.  But  do  not  yet  begin 
to  teach  him  to  count,  i.  c,  to  say  one,  two.  Expose 
now  three  fingers,  three  beans,  three  books,  etc.,  etc., 
in  various  collocations,  until  he  recognizes  a  triplet, 
under  any  disguise  of  form  ;  and  to  the  question  how 
many,  always  promptly  answers  three.  Review  now 
his  knowledge  of  two,  and  one  ;  and  when  there  is  no 
doubt  in  your  mind  that  he  knows  one,  three,  or  two, 
objects  of  any  kind,  in  any  position  to  be  one,  three, 
or  two,  you  add  a  new  element  as  follows  : — 

Place  a  finger  of  the  right  hand  in  front  of  one 
little  book,  of  the  left  hand  in  front  of  another ;  ask 
separately  concerning  each,  then  bringing  the  books 


ARITHMETIC.  .  4! 

and  hands  together  ask  of  both.  Then  put  the  ques- 
tion in  concrete  form,  one  finger  (showing  the  right 
hand),  and  one  finger  (bringing  up  the  left)  make  how 
many  fingers .-'  If  the  child  does  not  say,  at  once, 
two  ;  it  shows  that  he  had  not  learned  perfectly  the 
distinction  between  one  and  two,  and  you  must  begin 
again  with  the  first  exercise.  But  if  he  answers 
promptly,  then  is  your  opportunity  to  put  your  first  ab- 
stract question,  then  one  and  one  make  how  many  .-• 
and  he  will  answer,  two.  You  may  then  ask ;  And  if 
I  take  one  away  from  two  (suiting  the  action  to  the 
word)  it   will  leave   how  many  ? 

Many  teachers  will  pursue  this  method  of  nature  thus 
far  ;  but  its  great  value  can  be  really  appreciated  only 
by  one  who  will  follow  it  carefully  up,  at  least  as  far 
as  to  the  number  thirty.  This  will  require  time  and 
patience, — months  and  years  will  elapse, — but  the 
labor  will  be  abundantly  rewarded.  The  process  at 
first  should  be  very  slow,  and  the  child  should  be  led, 
somewhat  in  the  manner  I  have  indicated  above,  to 
see  for  himself  that  two  beans  and  one  bean  make 
three  beans  ;  one  from  three  leaves  two  ;  two  and  one 
make  three,  two  from  three  leaves  one  ;  one  and  one 
and  one  make  three.  Treat  each  number  successively 
in  the  same  manner  until  you  have  reached  six.  You 
may  now  arrange  a  series  of  little  parcels  of  beans,  or 
groups  of  chalk  dots,  in  order,  and  lead  the  child 
by  judicious  questions  to  see  that  the  numbers  four 
and  six  can  be  divided  into  twos,  and  the  number 
six  into  threes.  You  may  also  ask  him  to  name 
them    in    order,    and    lead    him    to    perceive    that 


42  TRUE    ORDER    OF    STUDIES. 

each  is  formed  by  adding  one  to  the  preceding.  Then 
giving  him  a  handful  of  beans  you  may  let  him  drop 
them  one  by  one  in  a  place  by  themselves,  naming  as 
each  one  drops,  the  number  which  he  thus  doles  out. 
Proceed  now  to  twelve,  slowly  and  gradually.  Great 
quickness  in  counting  may  be  produced,  without  strain 
on  the  child's  mind,  by  a  process  similar  to  that 
named  under  geometry  ;  expose,  successively, — for  a 
few  seconds  to  the  youngest,  for  a  fraction  of  a  second 
to  the  older  pupils — three,  two,  five,  six,  four,  one,  five, 
seven,  etc.,  objects,  and  see  who  can,  a  moment  after 
wards  name  the  number. 

By  the  time  that  you  have  reached  the  number 
twelve,  your  division  of  numbers  into  classes  may  be- 
gin to  receive  names.  The  numbers  that  can  be 
divided,  into  couples  of  beans,  without  leaving  an  odd 
one,  are  called  even  numbers  ;  those  that  leave  an  odd 
one,  are  odd  numbers.  Even  numbers  increase  by 
twos,  and  so  do  odd  numbers.  The  numbers  above 
twelve  being  too  large  to  be  recognized  at  sight,  may 
be  counted  by  addition  of  twos,  threes,  or  fours — and 
the  child  will  probably  find  that  he  has  been  thus  re- 
cognizing the  numbers  between  six  and  twelve,  by  ad- 
dition. The  commutative  principle  of  arithmetic  may 
be  shown  by  dividing  six  into  three  twos,  or  two  threes, 
still  using  beans.  With  the  same  illustrations,  before 
you  have  reached  the  number  thirty,  you  may  lead  the 
child  to  see  for  himself  the  difference  between  prime 
and  composite  numbers  ;  the  meaning  of  equal  factors; 
the  nature  of  powers  and  roots  ;  the  value  of  Eratos- 
thenes'  sieve,  and  its  defects  ;  the  distinction  between 


ARITHMETIC.  43 

the  two  factors,  that  one  is  abstract  and   the  other 
concrete,  etc.,  etc. 

The  little  primary  arithmetics  which  the  diligence 
of  our  writers  has  produced,  endeavoring  to  substitute 
pictures  for  real  objects,  in  giving  the  first  lessons  in 
numbers,  are  of  little  value  to  the  pupil,  and  do  much 
harm  to  the  teachers,  by  deluding  them  into  an  en- 
tirely false  view  of  the  functions  of  their  ofifice — a  view 
which  is  hardly  caricatured  in  the  jocose  anecdote  of 
the  teacher  who  gave  a  boy,  of  four  years,  the  three 
first  letters  of  the  alphabet  to  commit  to  memory  and 
recite  at  the  next  hour, — the  boy  never  yet  having  heard 
the  names  of  the  mysterious  symbols.  Text  books 
are  the  incubus  on  our  New  England  schools,  turning 
the  attention  of  the  teacher  and  the  child  away  from 
nature  and  from  truth,  to  fix  it  on  the  errors  and  weak- 
ness of  men.  Arithmetic  is  taught  backward,  begin- 
ing  with  reasoning  instead  of  with  observation,  and 
is  hampered  with  factitious  difficulties  or  artificial 
rules  and  processes.  I  have  known  but  three  really 
good  treatises  on  arithmetic  published  in  this  country, 
in  my  day  ;  one  of  these,  Warren  Colburn's  First  Les- 
sons, has  been  abused,  by  being  put  into  the  hands  of 
children  too  early,  and  has  thus  been  productive  of 
almost  as  much  harm  as  good  ;  a  second  was  promptly 
suppressed  by  legal  proceedings,  because  it  infringed 
on  Pliny  E.  Chase's  copyright ;  and  Chase's  Arith 
metic  has  gone  out  of  print,  and  the  stereotype  plates 
have  been  melted,  because  the  popularity  of  a  text 
book  in  America  is  in  inverse  proportion  to  its  real 
merits.      All  other    school    arithmetics    now    in    the 


44  TRUE    ORDER    OF    STUDIES. 

market  have  a  great  similarity  to  each  other  ;  the 
best  differing  but  slightly  from  the  average. 

Very  soon  after  the  child  has  become  familiar  with 
the  names  of  the  first  half  dozen  numbers,  and  can 
instantly  name,  without  conscious  counting,  any  num- 
ber of  beans  under  six,  he  should  be  taught  the  Arabic 
figures  representing  them,  and  from  that  time  should  be 
taught  to  write,  instantly,  the  figure  representing  the 
number  of  beans  exposed  to  view.  Quickness  in 
writing  numbers  should  now  be  cultivated  by  requir- 
ing the  children,  pencil  in  hand,  to  write  the  Arabic 
figures  on  the  slate,  as  you  successively  expose  for 
a  second  each  small  number  of  objects. 

Two  or  three  hundred  beans  may  now  be  arranged 
in  heaps  of  ten,  and  those  heaps  in  groups  of  ten,  and 
the  mysteries  of  decimal  notation  be  thus  made 
clear  to  sight.  The  rapidity  with  which  the  value  of 
the  units  in  the  different  places  increase  as  you  go  to 
the  left  will  never  be  distinctly  appreciated  until  the 
child  sees  for  itself,  in  the  heaps  of  beans,  how  few 
figures  are  needed  to  express  the  largest  quantities. 
When  he  has  perceived  this  he  will  comprehend  why 
men  need  names  only  as  high  as  millions. 

Then  break  up  a  few  dry  beans  and  select  pieces 
that  shall  average  about  one-tenth  of  a  bean  each,  and 
some  also  to  represent  hundredths,  and  he  will  see  in 
the  rapid  decrease  of  size,  why  we  so  seldom  need 
decimals  beyond  millionths.  Teach  him  from  this 
point  the  mode  of  writing  decimal  fractions,  without 
any  allusion  to  vulgar  fractions.  He  is  now  ready  for 
addition,  subtraction,  multiplication  and  division,  i)i 


ARITHMETIC.  45 

both  whole  numbers  and  decimal  fractions,  and  can 
learn  them  both  at  once,  as  easily  as  he  can  one  of 
them.  For  the  first  two  years  after  he  has  thus 
begun  to  cypher,  let  your  whole  aim  be  to  make  him 
expert  in  performing  these  four  operations.  Do  not 
ask  him  to  commit  any  rules  to  memory,  do  not  ask 
him  to  explain  or  understand  the  reasons  for  his  oper- 
ations, but  simply  keep  him  at  work  on  simple  ex- 
amples in  numbers,  whole  and  decimal.  Avoid  even 
giving  him  problems  that  shall  require  any  ingenuity 
in  reducing  them  to  form  ; — but  give  him  figures  to 
operate  upon,  and  tell  him  what  to  do,  until  the  mere 
addition,  subtraction,  multiplication  and  division  of 
whole  numbers,  or  decimals,  and  the  correct  pointing 
and  reading  them,  shall  be  an  automatic  process,  like 
the  reading  of  the  easiest  story  book. 

The  teacher  who  has  been  accustomed  to  the 
modern  erroneous  method  of  teaching  a  child  to  reason 
out  his  processes  from  the  beginning  may  be  assured 
that  this  method  of  gaining  facility  in  the  operations, 
before  attempting  to  explain  them,  is  the  method  of 
nature  ;  and  that  it  is  not  only  much  pleasanter  to 
the  child,  but  that  it  will  make  a  better  mathematician 
of  him.  In  this  work  of  cyphering  fast,  dictation  ex- 
ercises, like  Walton's,  are  of  great  value.  Especial 
attention  should  be  given  to  the  addition  of  columns, 
that  being  the  place  in  which  arithmetical  blunders 
most  frequently  occur.  A  convenient  method  is  to 
give  to  the  class  from  your  extempore  invention,  any 
odd  number  of  numbers,  each  beginning  in  the  same 
place,  keeping  a  record  of  them  ;  for  example,   248, 


46  TRUE    ORDER    OF    STUDIES. 

75 T. 6,  842,  943,  851.7:  then  give  the  arithmetical 
complements  of  all,  except  one  ;  for  example,  give  all 
but  the  second  one  above,  752,  158,  57,  148.3  ;  and 
then  say,  add.  The  class,  not  knowing  your  key,  can 
add  the  numbers  quicker  than  find  the  key  ;  you, 
knowing  the  key,  write  the  omitted  number,  7 $1.6,  and 
prefix  to  it  the  number  of  complements,  4,  giving 
instantly  the  sum,  4751.6;  and  you  are  ready  to  test 
at  once  the  accuracy  of  the  swiftest  computer. 
Similar  methods  are  easily  devised  for  the  other  rules. 
There  is  a  difficulty  in  a  child's  mind,  not 
usually  recognized  by  the  teacher,  in  passing  to  the 
application  of  number  to  continuous  quantity  ; 
and  one  of  the  minor  advantages  of  introducing 
decimal  fractions  into  the  very  beginning  of  written 
arithmetic,  consists  in  its  affording  a  ready  means  of 
introducing  the  idea  of  an  arbitrary  or  artificial  unit. 
Arrange  the  number  123.45  for  example  in  this  way; 
First  place  to  the  child's  left  a  group  of  ten  heaps,  ten 
beans  in  a  heap :  then  passing  to  the  right,  making 
another  group  of  two  heaps ;  still  further  to  his  right 
place  three  beans  ;  then  four  pieces  averaging  a  tenth 
of  a  bean  each  ;  and  lastly  to  the  right  lay  five  frag- 
ments of  bean  dust  for  hundredths.  Now  lead  him  to 
see  that  these  123.45  beans  may  be  written  as  1.2345 
groups,  or  as  12.345  heaps,  or  as  1234.5  tenths  of  a 
bean,  or  as  12345  hundredths  of  a  bean.  Repeat  this 
lesson,  varying  the  numbers,  day  after  day,  week  after 
week,  until  the  pupil  has  become  perfectly  familiar 
with  the  conception  of  varying  the  unit  from  groups, 
to  heaps,  to  beans,  and  to  hundredths.     Lead  them  by 


ARITHMETIC.  47 

judicious  questions  and  the  actual  exhibition  of  coin, 
to  see  that  1^12.375  may  in  like  manner  be  called 
1.2375  eagles,  or  123.75  dimes,  or  1237.5  cents,  or 
12375  mills.  Next  give  them  a  meter  stick,  and  show 
them  its  division  into  ten  decimeters  ;  100  centime- 
ters ;  and  its  possible  division  into  1000  millimeters, 
and  measuring  the  length  of  books,  tables,  window 
seats,  &c.,  in  the  school  room,  show  them  how  each 
can  be  expressed  in  terms  of  either  of  these  units  ; — 
and  the  passage  from  the  natural  to  the  artificial  unit 
will  have  been  made  unconsciously.  The  process 
should  however  be  continued  further,  by  learning,  from 
good  maps,  not  otherwise,  the  distance  from  the 
school  house  of  prominent  objects  in  the  neighbor 
hood,  other  schools,  churches,  banks,  hotels,  cross- 
roads, bridges,  &c.,  and  requiring  the  children  to  ex- 
press the  kilometers  as  meters,  centimeters,  and  by 
moving  the  decimal  point.  Be  careful  that  the  child 
has  a  definite  conception  or  image  of  the  length  of 
the  metre,  and  its  parts.  One  mode  of  doing  this 
is  to  allow  the  scholars  to  estimate  the  length  of 
various  objects,  and  then  test  the  accuracy  of  the 
estimate  by  applying  the  meter  stick.  A  little  rivalry 
in  this  matter  is  of  great  benefit  in  sharpening  the 
powers  of  observation  and  judgment. 

The  passage  from  linear  to  square  and  cubic 
measure  is  also  accompanied  with  more  difficulty,  in 
a  child's,  mind,  than  the  teacher  is  usually  aware  of. 
Indeed  we  seldom  find  even  an  adult,  except  in  certain 
professions,  who  has  a  really  practical  appreciation  of 
the  different  rates  of  increase  in  linear  dimensions, 


48  TRUE    ORDER    OF    STUDIES. 

surface,  and  solidity.  To  assist  the  pupil  in  gaining 
this  appreciation  it  is  well  to  have  a  square  meter 
permanently  marked  upon  the  blackboard  ;  and  also 
to  furnish  the  school  with  pieces  of  card,  one 
decimeter  square  ;  and  other  pieces  one  centimeter 
square.  Five  of  the  larger  pieces  of  card  will  thus 
give  the  means  of  making  a  litre  measure  in  cubic 
form,  which  ought  to  be  the  first  form  in  which  solid 
measures  are  introduced  to  a  child's  attention. 

We  are  thus  particular,  and  emphatic,  concerning 
the  early  steps  of  mathematical  education,  because  it 
is  "  the  first  step  which  costs."  Much  more  labor  is 
requisite  to  unlearn  than  to  learn.  As  we  have  be- 
Sore  said,  the  younger  the  class  of  pupils,  the  more 
need  of  a  high  moral  and  intellectual  character,  and 
of  peculiar  aptness  for  teaching  in  the  teacher.  The 
teachers  of  the  youngest  classes  ought  to  deserve  and 
to  receive  the  highest  wages. 

Fifty  years  ago  the  treatises  on  Arithmetic  were 
blind  guides,  giving  very  imperfect  announcement  of 
rules,  and  no  explanations.  In  the  modern  reaction 
the  opposite  extreme  has  been  reached.  Explana- 
tions, and  reasons,  and  pictured  illustrations,  have 
expanded  the  course  of  Arithmetics,  until  the  un- 
fortunate pupil  is  lost  in  a  wilderness  of  words,  and 
does  not  find  his  way  through  in  time  to  learn  to 
cypher.  The  science  of  Arithmetic  receives  so  much 
attention,  that  the  art  is  neglected  ;  and  the  elements 
of  the  science  are  so  much  expanded  that  its  higher 
parts  are  never  reached.  The  primary  object  in  the 
earlier  years,  from  7  to  12,  should   not  be  to  develop 


ARITHMETIC.  49 

the  reasoning  power,  but  to  give  familiarity  with  the 
forms  of  calculation ; — so  that  when  a  child  is  asked  a 
question,  he  should  not  begin  a  course  of  analysis  and 
reasoning  based  upon  a  model  in  the  text  book,  or 
given  by  the  teacher ;  but  should  begin  instantly  to 
add,  subtract,  multiply,  divide  the  numbers  themselves 
and  give  the  answer  in  numbers  instantly.  After  the 
age  of  12  he  may  begin  to  learn  to  explain,  using 
Warren  Colburn's  First  Lessons.  Life  is  not  long 
enough,  to  spend  so  large  a  proportion  of  it  on 
Arithmetic  as  is  spent  in  the  modern  system  of  teach- 
ing it ;  and  Arithmetic  is  too  valuable  an  art,  to  have 
our  children  neglect  to  acquire  facility  in  it,  while 
they  are  being  stupified,  and  disgusted  with  prema- 
ture attempts  to  understand  it  as  a  science. 

The  fewer  the  artificial  rules  in  Arithmetic,  the 
better.  Vulgar  fractions  must  always  be  retained  ; 
and  for  the  next  fifty  years  we  shall  need  English 
tables  of  weights  and  measures  ;  after  that  it  is  to  be 
hoped  that  they  will  drop  into  disuse,  as  the  shillings, 
nincpences,  fourpence-halfpcnnies,  fips  and  eleven- 
penny  bits  of  fifty  years  ago  have  given  place  to 
dollars  and  cents.  Square  root  and  cube  root  must 
also  be  retained  ;  and  it  were  very  desirable  to  re- 
introduce into  the  school  books  the  rule  of  Double 
Position,  as  a  natural  introduction  to  the  larger 
methods  of  modern  mathematical  science.  If,  at  the 
same  time,  four  place  logarithms  could  be  introduced, 
a  great  variety  of  problems  could  be  solved  interesting 
to  the  pupil,  and  stimulating  him  to  a  thirst  for  higher 
knowledge.     Logarithms  could  be   used  to  advantage 


50  TRUE    ORDER    OF    STUDIES. 

in  many  operations  of  business  life,  where  they  are 
now  neglected  :  and  would  be  used,  did  the  pupil  learn 
in  the  common  school  how  rapidly  and  easily  he 
attains  accurate  results  by  them.  For  the  child's  use 
three  place  tables  might  be  large  enough,  and  the 
cost  would  be  trifling.  The  labor  of  using  tables  in- 
creases very  rapidly  with  the  increase  of  decimal 
places  ;  and  it  is  a  point  of  practical  wisdom  to  use 
tables  of  a  size  proportioned  to  the  nature  of  your 
work.  Six  place  tables  seem  the  most  ill-judged  of  all ; 
being  too  unwieldy  for  ordinary  problems,  and  not 
nice  enough  for  nicer  operations. 


ALGEBRA.  5 1 


CHAPTER  V. 

ALGEBRA. 

ALGEBRA  was  originally  considered  an  exten- 
sion of  Arithmetic ;  and  its  essence  was 
supposed  to  consist  in  representing  numbers  by 
letters ;  so  that  we  could  represent-  an  unknown 
number  by  a  letter,  and  work  upon  it  as  if  known. 
This  is  still  the  best  way  of  introducing  the  pupil  to 
this  study.  And  it  were  well  if  part  of  the  time  saved 
by  reducing  Arithmetic  to  reasonable  bounds,  were 
given  to  acquiring  this  art.  There  is  no  difficulty  in 
teaching  the  scholars  in  the  Grammar  school,  as  they 
are  finishing  their  arithmetic,  the  meaning  of  the 
signs,  4-,  — ,  =,  (),  ()'^  and  the  like  ;  nor  in  teaching 
them  to  perform  their  arithmetical  examples  not  only 
on  the  numbers  given,  but  then  upon  letters  ;  obtain- 
ing thus  formulae,  in  which  again  they  may  substitute 
numbers. 

But  Sir  Isaac  Newton,  and  long  afterwards,  in  more 
distinct  form.  Sir  William  R.  Hamilton,  have  shown 
that  there  is  a  deeper,  a  more  vital  distinction  between 
algebra  and  arithmetic,  than  the  mere  ability  of  alge- 
bra to  deal  with  the  unknown  ;  it  deals  with  the  varia- 
ble ;  it  introduces  conceptions  of  flowing,  changing 
quantity  ;  it  is  in  fact  a  science  of  Time.     Leibnitz 


52  TRUE    ORDER    OF    STUDIES. 

then  introduced  what  Peirce,  in  his  Linear  Associative 
Algebra,  has  shown  to  be  a  new  algebra,  to  deal  with 
the  infinitesimal.  The  increase  of  power  given  by 
the  three  gifts,  Neper's  logarithms,  Newton's  doctrine 
of  fluxions,  and  Leibnitz's  algebra  of  the  calculus,  has 
been  incalculable.  Their  gifts  have,  however,  been 
but  scantily  used  by  the  compilers  of  elementary 
books,  until  within  the  last  half  century.  They  could 
be  advantageously  carried  much  further  ;  and,  in  spite 
of  the  famous  denial,  a  royal  road  to  geometry,  in  its 
widest  sense,  could  be  constructed  by  the  labors  of 
these  three  kings  ;  a  road  which  would  lead  to  new 
treasures  of  art  and  science  for  the  benefit  of  the 
whole  race. 

A  few  writers  on  geometry  have  followed  Peirce 
in  introducing  the  infinitesimal  into  the  elementary 
treatises  on  that  science  ;  it  is  to  be  hoped  that  others 
will  follow  him  and  go  beyond  him  in  introducing  the 
idea  of  flow  or  change  into  algebra.  An  anecdote  will 
illustrate  the  advantage  thus  to  be  derived.  A  pupil  of 
mine  had  labored  for  several  days  in  vain  to  under- 
stand the  demonstration  of  the  binomial  theorem.  I 
took  out  my  watch,  and  said  :  Now  give  me  undivided 
attention  for  five  minutes,  and  I  will  give  you  an  easier 
demonstration.  At  the  expiration  of  the  five  minutes,  I 
was  through  ;  and  he  was  repeating  with  all  the  de- 
light of  success,  my  demonstration.  In  those  five 
minutes  I  had  begun  deno'vo,irom  first  principles,  and 
given  him  a  simplification  of  Pcirce's  demonstration 
of  Arbogast's  Polynomial  Theorem,  based  on  deriva- 
tives, which  are  t!ie  same  as  differential  coefficients, 


ALGEBRA.  53 

or  fluxions.     I  had  avoided  every  new  technical  term, 
and  given  him  the  ideas. 

In  like  manner  by  introducing  the  idea  of  flow, 
early,  and  teaching  Leibnitz'  calculus  with  the  ordinary 
algebra,  the  whole  mysteries  of  trigonometry  and  an- 
alytical geometry  could  be  brought  within  the  range 
of  High  School  instruction  ;  what  might  be  done 
with  Hamilton's  Quaternions,  and  Ellis's  Stigmatic 
Geometry  I  have  not  examined.  The  mathematical 
sciences  are  advancing  with  wonderful  rapidity  in  this 
nineteenth  century;  —  but  our  American  common 
school  education  has  as  yet,  hardly  felt  even  the  discov- 
eries of  the  seventeenth.  I  would  at  least  bring  them 
up  to  the  position  of  that  era. 


54  TRUE    ORDER    OF    STUDIES. 


CHAPTER   VI. 
Physics. 

THE  CHILD  learns  from  its  earliest  experience 
some  of  the  mechanical  properties  of  matter  ; 
his  muscular  movements,  which  are  the  earliest  phe- 
nomena to  call  his  attention  to  the  existence  of  Space 
and  Time,  are  accompanied  also  by  a  sense  of  the  ex- 
ertion of  power,  and  of  an  external  resistance  to  that 
exertion.  The  introversion  of  consciousness  upon  his 
exertion  does  not  take  place  until  after  his  distinct  ap- 
prehension of  the  resistance.  The  degrees  of  resist- 
ance soon  give  him  conception  of  the  gaseous  fluid 
and  solid  states  of  the  body  ;  its  fixity  or  mobility, 
rest  or  motion.  At  the  same  time,  sight,  touch  and 
hearing  are  giving  him  with  his  primary  conception  of 
the  shape  of  different  objects,  ideas  also  of  light,  dark- 
ness, and  color ;  of  heat  and  cold  also  ;  and  of  smell, 
taste  and  flavor.  All  these  sensations  lead  to  new 
knowledge,  capable  of  scientific  development ;  which, 
however,  comes  later  than  that  in  mathematics. 

Frobel's  kindergarten  gifts  are  excellent  in  giving 
the  first  ideas  of  physics  as  well  as  mathematics.  All 
good  things  are,  however,  capable  of  perversion,  and 
there  is  danger  in  his  system,  as  in  all  others,  of  fall- 
ing into  a  routine  ;  endeavoring  to  bend  nature  to  our 


PHYSICS.  55 

system  ;  instead  of  making  our  practice  conform  to 
nature.  The  teaching  of  nature  is  incidental  and 
infinitely  varied.  By  incidental  I  mean  what  may 
be,  less  reverently,  called  accidental ;  it  is  teaching  by 
the  occurrences  of  the  hour.  The  mind  naturally 
passes  from  this  to  regular  and  systematic  study  ;  and 
we  obey  the  law  of  our  native  intellectual  power,  in 
preparing  scientifically  arranged  elementary  text  books. 
Nevertheless  the  earliest  teaching  of  nature  is  inciden- 
tal, and  it  will  be  found  that  in  no  other  way  can  we 
begin  the  study  of  the  sciences  successfully  in  our 
schools  than  by  incidental  teaching  ;  teaching  in  which 
the  teacher's  active  and  trained  mind  leads  the  child 
to  gain  knowledge  from  the  passing  events  of  each 
moment.  This  is  the  true  spirit  of  what  has  been 
called  object  teaching  ;  which  I  have  seen  degenerate 
in  the  hands  of  a  dull  and  lifeless  teacher,  into  a 
routine  as  worthless,  as  any  stereotyped  text  book. 

When  the  child  of  seven  or  eight  years  old  is 
building  with  little  wooden  bricks,  upon  his  covered 
desk,  the  teacher  will,  for  example,  have  the  oppor- 
tunity to  make  clear,  to  the  school,  some  of  the  principal 
properties  of  the  centre  of  gravity,  and  of  the  states 
of  stable  and  unstable  equilibrium.  He  will  not  give 
the  children  those  phrases,  but  will  lead  them  to  see 
that  if  the  centre  of  a  brick,  or  of  a  mass  of  bricks,  is 
not  supported  by  something  directly  under  it,  it  must 
fall ;  he  can  make  them  see  that  if  this  support  is 
narrow,  the  mass  is  easily  overthrown,  if  broad  it 
stands.  He  also  will  lead  them  to  a  practical  recogni- 
tion of  the  analytical  condition  of  stable  equilibrium  ; 


56  TRUE    ORDER    OF    STUDIES. 

that  if  on  a  slight  disturbance,  the  building  returns  tc 
its  former  position,  it  is  stable. 

The  laws  of  elasticities  also,  and  the  reflection  of 
motion,  may  be  exemplified  by  the  rebound  of  balls, 
the  return  of  echoes,  and  the  use  of  mirrors.  At  the 
age  of  eight  or  ten  years,  the  average  pupil  will  see 
and  appreciate  the  difference  between  the  more  per- 
fect elasticity  of  his  marbles,  and  the  less  perfect  of 
his  balls  ;  the  perfect  reflection  of  light  in  straight 
lines,  and  the  readily  refracted  ray  of  sound.  The 
games  with  balls  and  marbles,  illustrating  geometri- 
cally the  parabola,  and  the  ellipse,  give  us  also  the 
opportunity  for  incidental  instruction  concerning  the 
composition  of  forces,  the  effects  of  an  accelerating 
force,  the  ratio  of  momentum  to  velocity,  and  the  like. 
We  have  referred  to  the  effect  upon  a  boy's  mind  of 
the  truth  that  a  chain  supported  by  its  ends  can  be 
straight  only  when  vertical ;  a  similar  effect  is  pro- 
duced when  he  is  led  to  see  that  the  path  of  a  pro- 
jectile can  be  straight  only  when  it  is  a  perpendicular 
straight  line. 

Some  of  the  principal  laws  of  optics,  of  acoustics, 
and  of  thermotics  can  be  advantageously  given  to  the 
child  in  this  incidental  way.  The  optical  toys,  which 
are  in  almost  every  household  ;  musical  instruments, 
burning  glasses,  and  the  phenomena  of  dew,  rain, 
frost,  and  snow,  give  the  teacher  abundant  opportu- 
nities. The  lightning,  the  refractory  state  of  the  hair 
in  dry  cold  weather,  toy  magnets,  the  electric  fire 
alarm, — give  occasions  for  incidental  instruction  in 
electricity  and  magnetism. 


PHYSICS.  57 

In  giving  this  instruction  tell  the  child  only  what 
yo\i  really  know,  and  never  be  ashamed  to  confess 
your  ignorance.  Lead  him,  if  possible,  by  judicious 
questions  to  see  for  himself ; — when  not  possible,  tell 
him  clearly,  what  is  clear  to  you,  and  confess  ignor- 
ance as  to  the  rest.  A  popular  scientific  chattering 
upon  a  subject  is  worse  than  a  total  neglect  of  it. 
I  have  heard  a  lecturer,  to  whom  a  hundred  dollars 
was  paid  for  his  evening's  instruction,  tell  an  audience 
that  zinc  was  decomposed  by  sulphuric  acid,  and 
hydrogen  evolved  ;  that  a  certain  insect  in  the  sea 
ran  a  circular  saw  at  60,000  revolutions  a  second,  to 
cut  up  its  prey  ;  that  he  had  made  a  gyroscope, 
weighing  a  pound,  run  so  fast  as  to  weigh  but  five 
ounces.  A  text  book  on  Familiar  Science,  said  to 
have  sold  to  the  amount  of  nearly  200,000  copies  in 
the  United  States,  gives,  among  other  trash,  as  an  ex- 
planation why  soap  destroys  grease,  the  statement 
that  grease  consists  of  oleine  and  stearine,  and  that 
"  when  soda  or  potash  is  mixed  with  it,  the  oily 
principle  flics  off,  and  the  stearine  is  converted  into  an 
oxide  of  potassium,  which  is  perfectly  soluble  in 
water."  Such  instruction  as  this  would  be  improved 
by  the  substitution  of  Foote's  celebrated  passage  ; 
"  So  she  went  into  the  garden  to  cut  a  cabbage  leaf  to 
make  an  apple  pie,  and,  at  the  same  time,  a  great  she 
bear,  coming  up  the  street,  pops  its  head  into  the  shop. 
What,  NO  SOAP  .''  So  he  died,  and  she  very  impru- 
dently married  the  barber  !  "  The  absurdity  of  this 
would  be  laughable  ;  of  that,  is  lamentable. 

One  of  the  earliest  studies,  commencing  perhaps 


58  TRUE    ORDER    OF    STUDIES. 

at  the  age  of  seven  years,  should  be  geography.  Two 
modes  of  beginning  are  open  to  you.  The  first 
was  developed  in  Woodbridge's  geography.  You 
begin  with  the  school  room  and  draw  a  plan  of  it  on 
the  blackboard,  being  careful  to  put  the  north  side  of 
the  plan  up,  as  that  is  the  mode  universally  adopted 
in  maps.  While  looking  at  the  plan,  and  when  study- 
ing maps,  the  young  child  should  always  turn  in  his 
seat  until  he  faces  north  ;  the  older  child,  who  has 
learned  to  "  orient  himself  "  may  face  in  any  direction. 
When  the  plan  of  the  school  room  is  understood, 
draw  around  it  the  plan  of  the  school  yard ;  let  the 
children  copy  it ;  question  them  upon  it,  and  be  sure 
that  it  conveys  to  them  the  correct  impression.  Let 
them  measure  the  dimensions  of  the  room  and  yard, 
and  draw  the  plan  to  various  scales.  Add  now,  to 
the  plan  drawn  on  a  small  scale,  the  map  of  the 
neighboring  roads  and  streets,  and  let  the  pupils  indi- 
cate on  the  map  the  position  of  their  own  houses. 
Proceed  thus  gradually  to  show  them  the  map  of  the 
county,  of  the  state,  of  the  United  States  and  of 
North  America,  and  then  lead  them  to  the  globe. 

The  ether  method  is  the  one  which  I  have  usually 
pursued,  which  is,  to  begin  with  astronomy.  The 
heavens  catch  the  child's  attention  early,  and  he  wishes 
to  know  about  the  sun,  moon  and  stars.  The  only 
answer  that  can  be  made  to  his  inquiries,  in  this  age 
of  the  world,  is  to  explain  to  him  that  they  are  large 
balls,  and  to  tell  him  of  the  points  of  resemblance,  of 
the  moon  and  planets  to  this  terrestrial  ball.  Then 
show  him    a  globe,  (being  careful   to  have  the  pole 


I'livsics.  59 

pointing  towards  the  real  pole  in  the  heavens,  and  your 
own  meridian  uppermost,)  and  lay  a  marble  upon  it. 
Explain  to  him  that  the  earth  is  a  large  ball  or  globe, 
under  the  little  globe,  as  that  is  under  the  marble. 
The  immense  magnitude  of  the  great  globe  he  cannot 
as  yet  imagine  ;  and  at  first  you  must  be  content  to 
see  that  he  understands  its  form  and  motion.  Set  the 
globe  (rectified  as  before)  with  the  marble  upon  it,  in 
the  window  seat,  where  the  sun  may  shine  upon  it, 
and  draw  his  attention  to  the  fact  that  the  light  and 
shadow  on  the  marble  and  on  the  globe  are  similarly 
situated,  then  tell  him  that  the  light  and  shade 
fall  on  the  earth  as  they  do  on  the  marble  and 
on  the  globe,  making  night  in  the  shadow,  and  day  in 
the  sunshine.  Explain  how  the  reflection  from  the 
globe  diminishes  the  intensity  of  shadow  on  the 
marble  ;  that  reflection  from  the  window  seat  partially 
enlightens  the  under  side  of  the  globe.  Make  the 
amount  of  reflection  from  the  window  seat  more  ap- 
parent by  conveying  it  alternately  with  a  black  veil, 
and  a  white  handkerchief.  Now  explain  to  them  that 
"the  earth  hangeth  upon  nothing,"  floating  free  in 
space  like  a  bird  in  the  air  ;  and  that  is  the  reason 
why  the  night  is  so  much  darker  than  the  under  side 
of  the  little  globe  ;  namely,  because  there  is  no  win- 
dow seat  under  the  earth  to  cast  a  reflection  upon 
our  antipodes  ;  except  when  the  moon  acts  in  that 
office.  Take  the  children  out,  (in  the  morning,  when 
the  moon  is  in  its  last  quarter  ;  or  afternoon,  when  she 
is  in  the  first  quarter)  and  placing  a  globe,  ball,  or 
marble,  in  the  sunshine,  on  top  of  a  fence  or  post,  let 


6o  TRUE    ORDER    OF    STUDIES. 

the  children  successively  place  their  heads  in  a  posi- 
tion to  project  the  globe  against  the  moon  ;  they  will 
then  see  the  light  on  the  globe  will  take  the  shape  of 
the  moon.  Call  also  their  attention  to  the  fact  that 
the  moon  is  of  the  same  brightness,  by  day,  as  a  white 
cloud.  This  will  give  them  a  visible  demonstration 
that  the  sunlight  falls  on  the  planetary  bodies,  as  it 
does  on  the  marble  and  the  globe. 

Now  explain  to  the  child  the  figures  on  the  globe  ; 
which  is  meant  for  land,  which  for  water  :  and  show 
him  his  own  country  and  the  situation  of  his  own 
town  ; — still  remembering  never  to  direct  his  atten- 
tention  to  the  globe  until  it  is  i^ectified,  (bringing  the 
school  house  to  the  top  of  the  globe,  and  making  the 
North  Pole  point  north).  Give  him  brief  descriptions 
of  the  character  of  various  nations,  and  the  climate  of 
their  countries,  and  show  him  how  to  point  towards 
them,  by  putting  a  pencil  point  on  top  of  the  globe 
pointing  through  it  to  the  given  country,  and  explain- 
ing that  the  pencil  also  points  through  the  real  earth 
to  the  real  country.  The  magnitude  of  the  world  may 
also  be  given,  (the  great  circle  being  40,000  kilometers, 
and  the  diameter  being  12725  kilometers)  by  showing 
how  long  it  would  take  for  an  express  train  at  50 
kilometers  an  hour  to  go  round  ;  and  how  long  to  go 
at  a  slow  walk  of  5  kilometers.  Invite  the  children 
also  to  go  with  you  to  the  point  where  the  most  dis- 
tant point  can  be  observed,  and  show  them  on  your  re- 
turn to  the  school  house,  that  the  panorama  seen  from 
that  place  is  covered  by  a  very  small  spot  on  the 
globe.     Describe  to  them  the  highest  mountains  in 


PHYSICS.  6l 

the  world,  and  when  you  have  led  them  to  their  live- 
liest conceptions,  take  them  up  the  steepest  possible 
hill,  and  climbing  far  enough  to  show  them  some 
town  1 2  or  1 5  miles  distant,  point  out  to  them  how  small 
upon  the  globe  would  be  the  circle  of  their  vision. 
[The  square  root  of  seven  quarters  of  the  elevation 
of  the  eye,  in  feet,  is  the  radius  of  the  circle  of  vision 
in  miles.  The  square  root  of  fifteen  times  the  eleva- 
tion in  metres  is  the  radius  in  kilometers]. 

Place  again  the  marble  upon  the  surface  of  the 
globe,  (choose  a  mottled  or  marked  marble,)  and  hold- 
ing it  there,  show  them  that  the  rotation  of  the  globe 
rotates  the  marble  with  reference  to  the  sun,  but  not 
with  reference  to  the  globe  ;  that  the  marble  is,  like 
the  globe,  now  this  side  up,  now  that,  as  the  globe 
rotates  ;  but  the  marble  keeps  always  the  same  side  to 
the  globe.  Show  them  that  in  like  manner  if  the 
globe  stands  with  the  same  side  constantly  down,  that 
is,  towards  the  earth,  then  if  the  earth  rotates,  spins 
round,  the  globe,  and  the  marble,  balanced  on  top  of 
it  by  aid  of  a  few  grains  of  dust  or  crayon,  will  spin 
with  it.  Propose  now  to  see  whether  the  earth  is 
rotating  ;  by  placing  the  globe  (always  rectified)  in 
the  sun  shine,  noting  where  the  sun  light  falls, 
and  coming  at  the  end  of  the  next  half  hour  or  hour 
to  see  whether  it  has  moved.  When  the  children 
have  thus  seen  for  themselves  that  the  little  globe  is 
rotating  under  the  sun  at  the  rate  of  15*'  an  hour,  and 
the  marble  at  the  same  rate,  show  them  that  the  cause 
of  it  lies  in  the  great  globe  rotating  at  the  same 
velocity.     But  let  them  see  that  this  angular  velocity 


62  TRUE    ORDER    OF    STUDIES. 

implies  a  greater  speed  in  the  surface  of  the  great 
ball,  1 200  kilometers  an  hour,  or  nearly  that,  accoid- 
ing  to  the  latitude, — forty  times  railroad  speed  ;  so 
fast  is  their  school  house  constantly  whisking  east- 
ward. 

Now  show  them  that  by  placing  the  globe,  (rectified) 
in  the  sunshine  they  can  see  for  themselves  just 
where  the  sun  is  rising,  where  it  is  setting,  where  it  is 
on  the  meridian,  where  vertical,  and  so  on  ;  see  it  on 
the  globe,  and  thus  know  it  concerning  the  earth  ; 
they  will  be  greatly  charmed,  if  you  are  fortunate  in 
having  a  position  for  the  globe  in  which  it  can  remain 
some  hours  in  the  sun,  showing  them  from  hour  to 
hour,  as  they  return  to  it  after  other  occupations,  what 
countries  are  having  sunrise,  and  what  sunset.  Their 
attention  should  always  be  called  to  the  poles,  one 
lying  in  darkness,  the  other  in  light,  all  day  long. 
These  lessons,  with  the  smallest  kind  of  globe,  should 
be  repeated  in  every  month  of  the  school  year  ;  and 
thus  the  scholars  would  gain  precise  conceptions  of 
the  meaning  of  the  arctic  circle,  the  tropics  and 
equator,  the  causes  of  the  changing  seasons,  and  other 
matters  of  astronomical  geography,  more  surely  and 
accurately  than  in  any  other  way.  Especially  care 
should  be  taken,  for  this  end,  to  give  the  lesson  at  the 
equinoxes  and  solstices. 

From  the  globe,  the  transition  to  maps,  and  to 
detailed  geography  or  topography  is  easy  ;  and  in 
country  schools  may  be  made  intensely  interesting  to 
children  by  occasional  walks.  The  natural  objects 
actually  found  are  the  best  text  books  ;  the  brooks 


PHYSICS.  6;^ 

and  rivers,  the  various  soils,  and  rocks,  the  diverse 
kinds  of  vegetation,  the  roundness  of  the  earth  as 
seen  in  the  curve  of  water  Hues,  and  the  dip  of  the 
horizon  if  you  climb  a  hill ;  these  and  many  other 
points  will  readily  be  observed  by  a  child  when 
pointed  out ;  and  they  may  early  be  taught  also  to 
perceive  the  increased  beauty  given  to  the  landscape 
by  the  illusion  which  invariably  exaggerates  vertical 
heights  andunder-estimates  horizontal  distances.  Show 
them  that  this  makes  the  relief  maps,  with  their  ex- 
aggerated elevations,  so  true  to  the  feeling  of  nature. 
Let  them  also  learn  a  similar  lesson  by  building  clay 
models  of  the  hills  in  their  neighborhood,  upon  a  true 
and  then  on  an  exaggerated  vertical  scale. 

Further  lessons  in  Astronomy  should  be  given  by 
procuring  a  ball,  of  a  little  over  one  quarter  the 
diameter  of  the  globe,  and  holding  it  about  i  lo  times 
its  own  diameter  from  the  globe.  At  this  distance, 
it  will  appear  to  an  eye  held  close  to  the  globe,  of  the 
same  size  as  the  moon,  and  held  in  the  sunshine  may 
be  made  to  imitate  the  moon's  changes.  The  en- 
deavor, both  in  geography  and  astronomy,  should  be 
to  lead  the  child's  mind  away  from  the  illustration  to 
the  thing  illustrated.  It  is  annoying  to  see,  in  some 
of  the  best  geographies,  a  picture  of  the  earth  float- 
ing among  clouds,  some  of  which  are  larger  than  the 
diameter  of  the  earth.  Such  a  picture  will  make  it 
more,  instead  of  less,  difficult  for  the  child  to  get  a 
vivid  conception  of  the  real  facts, — that  the  atmos- 
phere and  clouds  make  a  covering  about  the  earth, 
about  as  thick  in  proportion  as  the  coating  of  varnish 


64  TRUE    ORDER    OF    STUDIES. 


I 


about  his  globe ;  that  the  highest  mountains,  and  the 
deepest  deep-sea  soundings,  are  but  like  the  uneven- 
nesses  in  the  grain  of  the  paper  with  which  the  globe  J 

is  covered.      Astronomy  is  the  most  powerful  among  * 

the  sciences,  in  developing  clearly  the  imagination  in 
space,  and  its  primary  facts  may  therefore  be  given 
to  children  many  years  before  they  can  understand 
the  processes  by  which  we  have  arrived  at  a  knowl- 
edge of  these  facts. 


CHEMISTRY.  65 


CHAPTER  VII. 

CHEMISTRY. 

CHEMICAL  relations  are  evidently  more  ab- 
struse than  mechanical.  It  requires  some 
maturity  of  mind  to  distinguish  chemical  compounds 
from  mere  mechanical  mixtures  ;  and  yet  the  simplest 
chemical  phenomena  begin  to  excite  a  child's  curiosity, 
by  the  time  that  he  is  ten  or  twelve  years  old  ;  and  it 
will  be  greatly  to  his  advantage  if  his  curiosity  is 
gratified  by  correct  explanation  and  sound  principles, 
instead  of  being  lulled  by  plausible  pretences  at  ex- 
planation. Oxidation,  especially  in  its  two  forms  of 
the  combustion  of  fuel  and  the  rusting  of  metals,  is 
the  most  prominent  instance  of  chemical  metamor- 
phosis that  the  child  will  notice.  A  skilful  teacher 
will  find  in  the  familiar  examples  of  this  metamor- 
phosis almost  daily  opportunity  for  incidental  instruc- 
tion in  the  fundamental  principles  of  chemical 
affinity,  atomic  proportions,  stability  or  instability  of 
compounds,  &c.  We  acknowledge  that  this  implies 
a  large  amount  of  intellectual  life  in  the  teacher,  but 
one  who  is  intrusted  with  the  direction  of  these 
earliest  movements  of  the  expanding  mind  should  be 
a  person  not  only  of  some  acquirements,  but  of  some 
intellectual  vivacity  ;  of  ability  to  seize  upon  the  right 


66  TRUE    ORDER    OF    STUDIES. 

occasion  and  right  moment  to  make  permanent 
lodgment  of  a  truth  in  the  child's  mind,  and  give  the 
child  a  new  ability  to  find  truth  for  itself.  There  is 
always  danger  of  a  bungling  teacher's  extinguishing  the 
child's  thirst  for  knowledge.  This  may  be  done  by 
diverting  the  attention  at  the  moment  when  interest 
has  been  aroused  ;  by  discouraging  with  difficulties, 
by  disgusting  with  tedium  ;  or  by  puffing  the  child 
into  a  conceit  that  he  has  learned  all,  when  he  had 
really  only  mastered  the  merest  rudiments.  The 
great  art  in  instruction  is  the  same  as,  in  letter  writing, 
according  to  Weller,  to  make  the  recipient  "wish 
there  was  more  of  it." 

A  boy  leaves  his  knife  out  in  the  rain,  and  brings 
It  in  red  with  rust,  another  takes  a  nail  out  of  the  fire, 
and  finds  it  nearly  all  converted  into  black  scales. 
The  anthracite  is  converted,  in  the  fire,  into  a  color- 
less air  which  flies  up  the  chimney,  and  a  few  ashes  ; 
but  about  the  fire  blue  blazes  are  seen.  The  com- 
bustion is  effected  by  a  double  process  on  part  of  the 
coal,  first  converting  it  into  one  kind  of  gas,  then  into 
another.  The  iron  is  oxidized,  into  black  scales  by 
the  fire,  into  red  powder  by  the  dampness.  The  child 
has  thus  before  him  two  examples  in  which  two  differ- 
ent compounds  are  made  with  the  same  simples,  and 
can  readily  deduce  from  them  important  corollaries. 
First,  that  the  same  element,  iron  for  example,  may 
be  concealed  under  various  forms ;  he  sees  the  metal, 
the  black  oxide,  and  the  red  ;  and  can  readily  under- 
stand when  you  show  him  pyrites,  copperas,  black  ink, 
and  other  instances  in  which  iron  lies  in  a  concealed 


CHEMISTRY.  6/ 

form.  Secondly,  that  substances  diverse  in  appear- 
ance, may  consist  of  precisely  the  same  elements,  in 
different  proportions.  Thirdly,  that  the  variation  of 
proportion  is  not  unlimited,  but  limited  to  a  few 
definite  proportions;  the  black  oxide  always  contain- 
ing yj-j  per  cent,  of  iron,  and  the  red  oxide  always  70 
per  cent.  Fourthly,  he  can  be  told  and  understand 
that  the  element  which  is  united  with  the  iron  in 
these  oxides,  is  the  same  as  that  which  unites  with 
the  coal  and  burns  it,  that  rusting  is  a  slow  burning. 
By  dropping  iron  filings  in  the  candle  blaze  he  can 
see  that  the  iron  may  be  made  to  burn  fast,  and 
brilliantly.  The  old  fashioned  flint  and  steel,  may 
show  the  same  thing,  and  also  illustrate  and  demon- 
strate that  heat  is  a  mode  of  a  motion ;  the  friction  of 
the  flint  scraping  off  a  fragment  of  steel,  so  rapidly  that 
the  motion  of  the  flint  produces  a  violent  vibration  in 
the  little  particles  of  the  fragment,  which  vibration  is 
heat.  Fifthly,  he  can  see  that  a  gas,  like  oxygen, 
may  make  a  solid  compound  with  iron,  a  gaseous 
compound  with  coal.  Sixthly,  he  can  thus  rise  to  the 
generalization  that  all  bodies  may  be  considered,  like 
water,  capable  of  existing  in  the  three  forms;  solid,  fluid 
and  gaseous.  Seventhly,  he  can  be  told  how  univer- 
sally and  abundantly  diffused  is  this  element  of 
oxygen,  constituting  one  fifth  of  the  air,  eight  ninths 
of  the  water,  and  one  half  of  the  solid  crust  of  the 
earth.  Such  are  a  few  of  the  chemical  lessons  which 
the  young  child  can  be  led  to  be  interested  in,  and  to 
learn,  from  the  familiar  incidents  of  burning  and 
rusting.     Many  other  daily  occurrences  may  lead  to 


68  TRUE    ORDER    OF    STUDIES. 

as  valuable  incidental  instruction  on  other  chemical 
facts  ;  and  prepare  the  pupil  for  the  higher  branches 
which  are  to  follow. 

It  will  be  observed  that  all  these  lessons  concern- 
ing difference  and  identity,  unity  and  multiplicity, 
definiteness  of  proportion,  and  limited  numbers  of  com- 
pounds, imply  clear  arithmetical  conceptions,  and 
that  therefore  arithmetic  precedes  chemistry  in 
the  hierarchy.  The  higher  branches  of  chemical 
philosophy  will  also  demand  geometry.  Few  bodies, 
for  example  are  absolutely  amorphous,  and  the  know- 
ledge of  crystalline  forms,  if  nothing  else,  is  required 
in  distinguishing  chemical  compounds.  Remember, 
in  every  branch  to  teach  humility,  and  let  the  child  see 
that  he  is  getting  only  glimpses  of  a  boundless  field. 


MINERALOGY.  69 


CHAPTER    VIII. 

MINERALOGY. 

A  PRELIMINARY  knowledge  of  the  meaning 
of  chemical  relations  having  been  acquired,  the 
pupil  is  ready  to  classify  the  substances  actually  found 
in  nature.  In  the  "  Evenings  at  Home  "  of  Dr.  Aiken 
and  his  sister,  are  some  admirable  examples  of  early 
lessons  in  mineralogy,  botany  and  zoology.  The 
"  Harry  and  Lucy "  of  Maria  Edgeworth  contains 
equally  valuable  lessons,  and  a  school  teacher  may 
find  aid  in  learning  how  to  present  scientific  truths  to 
the  child  from  these  works. 

Among  the  early  incidental  teaching  in  miner- 
alogy will  be  the  introduction  to  the  group  of  metals  ; 
those  anciently  known,  together  with  the  modern 
platinum,  nickel,  antimony,  bismuth,  and  aluminium, 
can  readily  be  furnished  to  every  school  house. 
Alloys  may  be  shown  in  sufficient  number  to  illustrate 
their  nature ;  especially  brass,  bronze,  pewter,  and 
other  commercially  important  mixtures.  The  mode 
of  obtaining  these  metals,  from  their  ores,  and  the 
chemical  nature  of  their  ores  ;  mechanical  properties, 
uses  in  the  arts,  and  in  medicinis  ;  history  of  their 
discovery,  and  the  like  will  furnish  many  topics  for 
conversation.       The    usefulness    of   iron    alone,    will 


7©  TRUE    ORDER    OF    STUDIES. 

furnish  food  for  many  hours  at  different  times.  The 
rarer  metals  may  less  seldom  be  shown  ;  but  some 
of  them,  as  sodium,  potassium,  calcium,  lithium, 
osmium  and  iridium,  will  be  so  naturally  suggested 
to  the  teacher's  mind,  by  familiar  objects  in  the  school 
room  that  she  can  hardly  avoid  telling  the  children 
something  about  them. 

When  a  school  is  situated  in  the  country,  especi- 
ally when  that  country  is  rich  in  a  variety  of  minerals, 
the  scholars  should  be  invited  to  bring,  to  the  school 
room  specimens  of  all  that  they  can  find  in  their 
Saturday  rambles.  The  different  kinds  of  rock  and 
earths,  should  be  referred  to  their  nearest  species ; 
and  the  uses  of  each  kind,  in  building,  plastering, 
making  brick,  farming,  and  so  on,  should  be  explained. 
There  will  always  be  some  one  in  the  school  district 
or  in  the  town  to  whom  the  teacher  can  apply  for 
information  if  the  child  chances  to  bring  in  an  un- 
recognised specimen.  When  the  mineral  is  crystal- 
line in  its  form,  be  careful  to  draw  the  attention  of  the 
pupil  to  its  precise  shape,  even  to  the  minutest 
feature.  When  the  mineral  is  amorphous  call  attention 
to  that  fact. 

Gases  do  not  present,  in  visible  natural  forms,  any 
great  variety  ;  but  the  four  or  five  elements  constantly 
found  in  the  atmosphere,  with  one  of  which  his 
chemical  studies  began,  may  be  described. 


PHYSIOLOGY,  71 


CHAPTER  IX. 

PHYSIOLOGY. 

THE  legislatures  of  our  various  States,  and  even 
their  Committees  on  Education,  are  not  infallible. 
To  require  instruction  in  physiology  in  the  common 
school,  as  ordinarily  constituted,  is  to  require  babies 
to  make  bricks,  and  that  without  straw.  The  super- 
ficial thinker,  readily  perceiving  the  mode  in  which 
arithmetic  is  applicable  to  practical  life,  exaggerates 
the  value  of  the  study  as  a  means  of  education,  and 
defeats  his  own  end  ;  not  even  teaching  the  child  to 
cypher  as  well  as  he  would  do,  were  arithmetic  con- 
fined to  its  proper  narrow  boundaries.  In  like  man- 
ner because  the  application  of  human  anatomy  and 
physiology  to  the  practical  care  of  the  health,  is  ob- 
vious, many  teachers  and  legislators  have  pressed  with 
great  zeal  the  introduction  of  those  studies  into  the 
primary  schools.  But  the  study  of  the  human  body 
and  its  functions  can  be  made  much  more  effective, 
more  interesting,  and  more  valuable,  if  it  is  preceded 
by  lessons  upon  zoology  and  botany.  In  the  order  of 
nature,  the  plant  lives  upon  inorganic  food,,  and  the 
study  of  vegetable  physiology,  must  come  after  the 
study  of  mineralogy  ;  the  animal  lives  upon  the  plant, 
and  vegetable  physiology  must  precede  animal.     In 


72  TRUE    ORDER    OF    STUDIES 

the  order  of  nature  the  child's  attention  is  most  forcibly 
attracted  by  what  is  external  ;  and  by  what  is  foreign 
to  his  own  body,  before  it  is  by  his  own  members.  It 
is  an  unnatural,  an  injurious  thing  to  turn  the  child's 
attention  too  early  to  the  functions  of  his  own  organs. 
A  better  result,  both  intellectually  and  morally,  will 
be  attained,  if  the  teachers  and  parents  take  care  of  the 
diet  and  exercise  of  the  child  ;  his  clothing,  and  the 
temperature  and  ventilation  of  the  rooms  in  which  he 
sleeps  and  studies  ;  at  least  until  the  age  of  thirteen 
to  fifteen  years.  It  must  be  confessed  that  teachers 
and  parents  are  themselves  sometimes  terribly  ignor- 
ant, or  perverse,  upon  such  subjects.  I  have  seen, 
highly  educated  and  cultivated  people  urging  mere  in- 
fants to  eat  rich  cakes  and  scalloped  oysters  ;  and 
giving  cakes  and  candies  to  older  children  between 
meals.  Nevertheless  the  cure  for  such  terrible  abuses 
is  not  to  be  found  in  teaching  physiology  to  children, 
but  in  teaching  it  to  young  men  and  young  women, 
before  they  have  the  care  of  children  providentially 
intrusted  to  them. 

The  mind  must  be  prepared  for  understanding 
physiology,  by  previous  instruction  in  botany  and 
zoology ;  and  the  observing  powers  being  at  the  same 
time  thus  developed,  will  prevent  the  danger  that  the 
introduction  of  anatomy  and  physiology  will  lead  to 
premature  and  excessive  habits  of  mental  introversion. 
The  study  of  one's  own  body  approaches  nearer  to 
psychology,  forming  a  natural  introduction  to  it ;  and 
should,  therefore,  come  last  among  the  studies  of 
Natural  History.     I  mean  to  say  that  the  study  of 


PHYSIOLOGV.  73 

human  anatomy  and  physiology  naturally  and  inevit- 
ably leads  a  child  to  make  psychological  investigations 
into  the  facts  of  consciousness,  involved  in  the  exer- 
cise of  the  functions  of  his  own  frame  ;  and  this  is  not 
a  wholesome  process  for  him  before  the  age  of  four- 
teen or  fifteen  years,  if  even  so  early. 

4 


74  TRUE   ORDER  OF    STUDIES. 


CHAPTER  X. 

BOTANY. 

INASMUCH  as  botany,  although  it  depends  upon 
chemistry  in  its  physiological  department,  classifies 
plants  solely  by  their  texture  and  form,  some  knowl- 
edge of  the  common  weeds,  and  flowers,  the  trees, 
grasses,  mosses  and  lichens,  of  the  neighborhood,  may 
advantageously  be  given  to  a  child  as  soon  as  it  is  old 
enough  to  distinguish  them.  Even  in  the  cities  the 
shade  trees,  gardens,  and  yards  offer  an  opportunity 
for  gathering  specimens.  In  walking  from  Franklin 
street,  through  Arch  to  Summer  street,  Boston, — not 
more,  I  suppose,  than  125  or  150  meters,  in  thickly 
frequented  streets, — I  saw  thirteen  different  species 
of  plants,  crouching  against  the  foot  of  the  walls,  and 
rooting  between  the  bricks  of  the  pavement.  It  was 
thirty  years  since,  and  I  do  not  recall  them,  but  pre- 
sume there  were  two  or  three  mosses,  two  or  three 
lichens,  as  many  grasses,  and  perhaps  shepherds' 
purse,  knot  grass,  wild  pepper  grass  and  plantain,  with 
one  or  two  clovers.  Linnaeus  is  said  to  have  found 
81  species  in  a  square  yard.  One  might  say  of  plants 
what  Professor  Cleveland  used  to  say  of  minerals  : 
"  You  can  find  almost  any  species  in  Topsham,  if  you 
will  look  for  it." 


Los  Ange,. 
BOTANY.  75 

From  the  day  that  a  child  enters  the  sub-primary 
school,  I  would  have  it  receive  oral  instruction  in 
botany  ;  illustrated  when  possible,  by  living  plants  ; 
if  not,  by  pressed  plants,  or  even  by  good  drawings. 
At  first  the  child  may  be  simply  taught  to  recognize 
different  species  at  sight ;  just  as  he  knows  a  man,  a 
woman,  a  horse  or  a  dog  ;  that  is,  he  may  simply  learn 
to  say  on  seeing  the  plants  :  This  is  a  sugar  maple  ; 
this  a  Norway  maple  ;  this  is  a  lilac  ;  that  a  white  birch ; 
this  a  white  pine  ;  that  a  yellow  pine  ;  this  a  sweet 
violet  ;  that  a  bird-foot  violet.  Afterwards  he  may 
have  a  sprig  of  sugar  maple,  and  one  of  Norway 
maple,  given  to  him  to  study.  Let  the  class  look  long 
and  carefully  at  specimens  of  two  allied  species,  and 
then  try  which  one  can  point  out  the  most,  or  the 
most  important,  of  the  differences  between  the  two. 

In  the,first  volume  of  Agassiz's  Contributions  to  the 
Natural  History  of  the  United  States,  he  gives  an 
essay  on  the  principles  of  zoological  classification. 
He  shows  that  the  animal  world  is  first  of  all  divided 
into  four  distinct  plans  of  structure.  Zoologists  who 
believe  in  gradual  evolution  attempt  to  belittle  the  im- 
portance and  accuracy  of  this  division  into  four  plans, 
but  it  rests  on  necessary  mathematical  foundations  ; 
and  the  glory  of  Cuvier  will  not  pale  before  that  of 
Darwin.  Each  of  these  four  great  branches  is,  ac- 
cording to  Agassiz,  divided  into  classes,  according  to 
the  means  employed  in  carrying  out  the  plan  of  its 
structure.  Each  class  is  again  divided  into  orders, 
according  to  the  general  degree  of  complexity  or  sim- 
plicity  of  the   organization.      Each  order   is    again 


^6  TRUE    ORDER    OF    STUDIES. 

divided  into  families,  distinguished  from  each  other  by 
the  general  outline  of  their  external  form.  Each 
family  is  divided  into  genera,  distinguished  from  each 
other  by  the  anatomical  detail  of  the  feet  and  mouth. 
Each  genus  is  divided  into  species,  distinguished  from 
each  other,  by  the  difference  of  their  relations  to  the 
external  world,  and  to  members  of  their  own  species. 

No  botanist  has  done  for  plants  what  Agassiz  has 
thus  done  for  animals.  Yet  there  is,  doubtless,  a  close 
analogy  in  the  principles  of  classification  that  must  be 
adopted  in  botany  to  those  that  hold  in  zoology.  And 
as  in  animals  the  easiest  division  for  a  child  to  recog- 
nize is  that  of  families,  because  it  depends  upon  ex- 
ternal form  ;  so  among  plants,  the  child  will  more 
readily  appreciate  the  likeness  among  members  of  a 
well  defined  natural  family,  or  tribe,  than  any  other 
botanical  likeness.  I  have  known  a  child  of  very 
tender  years,  and  not  at  all  distinguished  for  accuracy 
of  observation,  call  a  succory  flower,  at  first  sight,  a 
blue  dandelion. 

When,  therefore,  the  child  is  able  to  point  out 
similarities  and  differences,  from  its  own  independent 
observation,  between  different  flowers  which  it  brings 
in,  it  may  be  taught  to  observe  family  likenesses  ;  to 
see,  for  example,  the  relationship  of  the  oak  to  the 
hazel,  in  their  catkins  of  staminate  flowers,  and  the 
involucre  surrounding  the  nut  ;  or  the  kindred  of  the 
alder  to  the  birch  in  having  both  kinds  of  flowers  in 
scaly  catkins,  with  two  or  three  flowers  under  each 
scale.  The  greatest  care  must  be  taken  not  to  allow 
the  child  to  think  that  a  few  words  embody  all   the 


BOTANY.  'J'J 

points  of  resemblance  which  characterize  a  family. 
He  must  ever  be  led  to  perceive  the  unity  of  each 
organism  ;  that  the  oak  and  the  hazel,  for  example, 
differ  from  each  other  in  every  single  point  wherein 
they  can  be  compared  ;  yet  have  also  a  certain  family 
likeness  in  every  part  ;  and  his  definitions  simply 
seize  upon  the  likenesses  that  are  easiest  to  describe, 
not  upon  those  which  are  most  vital. 

Much  less  should  the  child  be  encouraged  or  even 
permitted  to  repeat  formulas  on  such  subjects  by  rote. 
The  very  objects  for  which  such  studies  are  intro- 
duced into  our  schools  is  defeated  when  the  children 
are  allowed  to  commit  the  words  of  the  text  book  to 
memory.  Yet  so  accustomed  are  some  teachers  to 
this  mode  of  instruction  ;  so  incapable,  apparently,  of 
conceiving  of  any  better  plan,  that  I  have  known 
teachers  to  require  their  pupils  to  repeat  the  very 
words  of  Dr.  Gray's  "  How  Plants  Grow,"  and  of  my 
own  "  First  Lessons  in  Geometry."  I  have  no  doubt 
that  Miss  Hall,  "  Our  World,"  Miss  Youman's 
"  First  Lessons  in  Botany,"  and  Prof.  E.  S.  Morse's 
"  First  Book  of  Zoology,"  are  abused  in  the  same 
manner,  so  difficult  is  it  for  teachers  to  understand 
that  the  natural  objects  themselves  are  the  true  text- 
books ;  and  that  the  words  written  by  men  are 
nothing  in  comparison  with  the  lines  of  nature,  whence 
the  true  man  of  science  gets  all  that  he  can  record. 

By  having  the  children  collect  and  bring  to  the 
school-room  the  common  flowers  and  weeds  of  tneir 
neighborhood  ;  and  by  leading  them  to  examine  and 
compare  the  flowers  and  seed  vessels  (and  to  some 


78  TRUE    ORDER    OF    STUDIES. 

extent  the  foliage  also),  they  can,  without  the  slightest 
strain  upon  their  mind,  or  memory,  before  they  are 
fourteen  years  old,  be  taught  to  recognize  at  sight  any 
one  of  three  or  four  hundred  common  species  ;  and  to 
refer  the  greater  part  of  them,  at  once,  to  their  natural 
families,  and  recall  the  principal  characters  of  the 
family  and  its  uses  in  the  arts  and  in  medicine.  No 
book  need  be  placed  in  their  hands.  The  teacher 
should  have  Dr.  Gray's  books,  and  any  others  as  ad- 
juncts, to  refer  to  as  a  basis  of  oral  instruction  ;  but 
the  child  should  study  the  living  plants,  or  dried  ones, 
or  good  drawings.  I  am  speaking  of  the  sub-primary 
school  ;  the  instruction  of  older  pupils  is  less  difficult 
and  less  important. 


ZOOLOGY.  79 


CHAPTER  XL 

ZOOLOGY. 

ZOOLOGY  is  not  forced  upon  the  child's  atten- 
tion by  nature  so  constantly  as  botany.  The 
plants  stand  to  be  examined  at  every  step  of  his  path- 
way. Yet  the  motion  of  animals,  and  still  more,  their 
intelligence,  makes  them  more  interesting  and  fascin- 
ating to  most  children  than  plants.  And  although 
physiology  demands  a  knowledge  of  chemistry,  yet  the 
classification  of  animals,  like  that  of  plants,  depends 
primarily  upon  their  organic  structure,  their  external 
form,  and  upon  their  manifest  relations  to  the  exter- 
nal world.  A  child  of  five  years  old  is  interested  in 
watching  animals  ;  and  I  have  even  known  a  child  of 
half  that  age  to  watch  insects  and  toads  with  the 
closest  attention,  again  and  again,  patiently  observing 
their  habits  ;  and  he  may  readily  be  taught  to  dis- 
tinguish and  name  many  of  the  creatures  which  he 
thus  observes. 

In  a  country  school-house,  in  the  month  of  May  or 
June,  it  frequently  happens  that  the  notes  of  thirty  or 
forty  different  species  of  birds  are  heard  in  the  course 
of  a  single  day.  It  would  be  no  waste  of  time,  but  on 
ihe  contrary,  a  thing  of  inestimable  value,  should  the 
teacher  enable  his  pupils  to  recognise  each  species  by 


80  TRUE    ORDER   OF    STUDIES. 

teaching  them  to  learn  their  appearance  also  and  hab- 
its  ;  and  perhaps  tell  them  the  family  to  which  each 
belongs. 

In  teaching  the  names  of  birds  and  flowers  there 
is  a  great  difficulty  which  we  may  as  well  boldly  face. 
When  the  child  has  learned  to  recognise  a  plant  or  an 
animal  at  sight,  it  becomes  almost  a  necessity  to  give 
him  a  name  for  it ;  if  you  do  not,  he  will  name  it  for 
himself.  But  many  of  our  familiar  weeds  and  birds 
have  no  common  names ;  the  common  names  of  many 
are  also  very  inappropriate.  English  names  are  given 
to  our  American  objects ;  and  when  the  child  reads, 
in  his  school-books,  selections  from  English  literature, 
he  brings  up  a  wrong  picture  of  American  instead  of 
English  scenery.  Adults  of  some  culture,  are  con- 
stantly subjected  to  the  same  cause  of  error.  In  one 
of  Wilson  Flagg's  interesting  volumes  he  confuses  the 
Roxbury  Waxwork  {Celastriis  scandetis)  with  Bitter- 
sweet {Solamcm  dulcamara),  attributing  the  medical 
properties  of  the  latter  to  the  former  ;  and  I  have 
known  others  hearing  the  Bittersweet  {S.  dulcamara) 
called  J3eadly  Nightshade,  immediately  assume  that 
it  was  Belladonna.  Thus,  also,  the  name  of  Wood- 
bine (fragrant  monthly  honeysuckle)  is  in  this  country 
given  to  the  Virginia  creeper,  which  is  a  sort  of  five- 
leaved  grape  ;  the  name  robin  is  given  to  a  thrush  ; 
the  name  ivy  to  a  poisonous  climbing  sumac  ;  the 
name  pennyroyal  to  a  plant  which  smells  like  it 
Other  common  names  are  worthless  from  either  being 
local,  or  from  being  differently  applied  in  different 
States  of    the    Union.     Thus,    our   American   plant 


ZOOLOGY.  81 

Gaultheria,  is  called  in  some  sections  Wintcrgreen,  in 
others  Chequerberry,  in  others  Pine  Ivy,  in  others 
Partridge-berry,  in  others  Tea-berry.  And  the  English 
word  honeysuckle  is  applied  not  only  to  the  genus 
and  family  of  the  Woodbine  ;  but  in  various  parts  of 
the  United  States  is  given  to  Azaleas,  Diervillas,  Colum- 
bines, and  Clovers.  In  one  of  Emerson's  poems  he 
speaks  of  "  blinding  dogwood  "  ;  by  which,  as  a  New 
England  man,  he  means  the  poisonous  Swamp  Sumac  ; 
hut  a  man  of  the  middle  Western  States  would  be 
greatly  perplexed  to  know  why  Emerson  should  call 
the  beautiful  flowering  and  cornel   "  blinding." 

The  common  names  of  fishes,  and  of  birds  are  in 
this  country  in  the  same  state  of  confusion  ;  the  fishes 
perhaps  even  worse.  Care  should  be  taken  with  child" 
ren  to  give  them  from  their  earliest  acquaintance  with 
the  plant  or  animal,  a  name  which  will  not  thus  mis- 
lead. Let  them  understand  that  our  pennyroyal  is 
"  American  "  and  different  from  the  European  ;  that 
our  lark  is  not  the  singing  lark  of  which  English  poets 
speak  ;  that  our  robin  is  not  the  robin-redbreast  of  the 
old  world,  but  is  more  like  a  thrush  ;  and  that  our  blue 
bird  is  nearer  being  a  blue-breasted  robin.  I  hardly 
need  say  that  the  child  should  be  taught  to  call  a 
columbine  by  its  name  ;  and  reserve  the  word  honey- 
suckle for  the  genus  Lonicera  and  its  closest  con- 
geners. Nor  need  the  teacher  fear  giving,  where  there 
is  no  good  common  name,  the  scientific  name.  Many 
scientific  names,  (such  as  geranium,  fuchsia,  eschscholt- 
zia,  clarkia,  abutilon,  althea,  syringa,  rose,  violet, 
crocus,)  are  as  familiar  to  lovers  of  flowers  as  any  com- 


82  TRUE    ORDER    OF    STUDIES. 

mon  names  can  be.  If  the  child  hears  no  other  than 
the  scientific  name  he  remembers  it  as  readily  as  he 
will  an  English  name. 

Poets  have  sometimes  expressed  the  fear  lest  a 
scientific  acquaintance  with  nature  should  destroy  its 
beauty  ;  lest  the  song  of  the  bird  might  seem  less 
melodious  if  you  called  the  songster  by  a  barbarous 
Latin  name.  On  the  contrary,  a  closer  acquaintance 
with  nature  only  increases  the  pleasure  of  one  who 
truly  loves  her.  The  beau' if ul  in  nature  is  always 
more  beautiful  than  it  at  first  appears  to  us  ;  and  if 
we  lose  our  appreciation  of  it,  the  fault  is  in  us  and  not 
in  the  object.  "  Nature,"  says  the  Concord  seer, 
"  never  became  a  toy  to  a  wise  spirit."  The  wisdom 
and  beauty  embodied  in  each  specimen  of  organic  life, 
is  "not  only  vast,  but  infinite  ";  so  that  there  is  no 
possibility  of  the  closest  study  exhausting  it. 

The  insects  in  any  given  country  are  usually  more 
numerous,  in  species,  than  the  plants.  The  mysteries 
of  insect  transformation,  the  wonderful  mechanical 
instincts  that  many  of  them  display,  the  brilliancy  of 
the  colors  of  some,  and  the  pertinacity  with  which 
others  thrust  themselves  upon  the  attention  of  man, 
render  insects  peculiarly  fitted  to  engage  a  child's  at- 
tention, and  to  serve  as  a  basis  for  "  incidental "  in- 
struction in  zoology.  In  this  class  of  animals  the 
orders  are  more  conspicuously  distinguished  than  the 
families  ;  and  for  con.enience,  in  talking  about  the 
specimens  which  are  brought  in,  it  may  be  best  to 
group  them  at  first  simply  in  orders.  They  are,  in 
general,  easily  preserved,  and   I  would  have,  in  every 

4* 


ZOOLOGY.  85 

primary  school,  a  collection  of  the  most  common 
species  of  the  neighborhood,  scientifically  arranged  in 
boxes  with  cork  bottoms  and  glass  tops.  These  would 
be  better  than  books,  to  serve  as  a  reference  for  any 
insects  which  the  children  might  catch  and  bring  in. 

The  field  of  zoology  is  vast,  and  even  entomology 
is  more  than  sufficient  to  occupy  a  lifetime.  Yet  on 
account  of  this  very  magnitude  of  the  field,  the  child's 
attention  should  be  early  directed  to  it ;  so  that,  if  it 
be  one  for  which  he  proves  peculiarly  adapted,  he 
may  have  the  advantage  of  an  early  beginning.  But 
whether  he  pursue  it  in  after  life  or  not,  the  study  of 
zoology  and  botany  in  the  earliest  years  is  important 
for  the  intellectual  discipline  which  it  gives.  In  the 
erroneous  education  of  the  present  day,  intellectual 
discipline  is  supposed  to  be  needed  only  for  the 
reasoning  powers ;  whereas  it  is  needed  for  all  the 
faculties  ;  the  observing  and  the  imaginative  as  well 
as  the  reasoning;  and  should  be  given  in  that  order, 
the  child  being  first  of  all  taught  to  observe,  to  see 
with  the  outward  eye.  The  main  object  of  these  first 
lessons  in  natural  science  is  to  induce  the  spirit  of 
patient  exactness  in  observation  ;  calling  the  child's 
attention  to  differences  as  carefully  as  to  likenesses, 
and  to  the  fact  that  likeness  in  one  part  my  co-exist 
with  diversity  in  another ;  that  the  likeness  may  be 
conspicuous  and  the  difference  obscure  ;  or  on  the 
other  hand,  the  differences  obvious,  and  the  likeness 
in  miniature.  Nevertheless,  while  the  main  object  is 
to  cultivate  a  spirit  of  observing  patiently  and  accu- 
rately for  oneself,  a  second  object   is  not  to  be  lost 


84  TRUE    ORDER    OF    STUDIES. 

sight  of  ;  which  is  to  place  incidentally,  as  opportunity 
offers,  before  the  mind  of  the  pupil,  general  principles, 
already  discovered,  and  firmly  established  by  the 
inductive  philosophy  ;  principles  which  may  assist  the 
pupil  in  the  guidance  of  both  his  sense  and  his  reason, 
in  his  future  studies,  and  in  his  daily  business. 

The  evils  of  introducing  the  child  too  early  to  the 
consideration  of  human  physiology  have  been  already 
mentioned.  Comparative  anatomy  will  be  usefully 
introduced  to  his  notice  much  earlier.  The  homology 
of  the  parts  in  vertebrate  animals  with  those  of  his 
own  body,  forces  itself  on  the  attention  of  the  youngest 
child  who  plays  with  a  kitten,  or  watches  a  toad.  He 
may  readily  be  led  to  see  the  homology  in  the  more 
remote  forms,  even  in  the  fishes,  while  the  difference 
between  the  limbs  of  the  vertebrates,  and  the  organs 
of  locomotion  in  the  invertebrates  must  also  be  care- 
fully pointed  out.  Thus  these  studies  will  gradually 
develope,  without  conscious  effort  on  the  part  of  pupil 
or  teacher,  a  power  of  judgment  and  of  reasoning  in- 
dependent of  forms  of  language. 

Prominent  among  the  reasons  why  the  studies  of 
Natural  History  should  be  introduced  into  the  primary 
schools,  is  the  fact  that  it  accords  with  the  usual  tastes 
of  children,  as  well  as  with  the  natural  order  of  intel- 
lectual development.  Children  are  always  interested 
in  looking  at  crystals,  plants,  flowers,  insects,  shells, 
birds,  and  beasts  ;  they  are  interested  in  intellectual 
and  spiritual  truths  only  when  dressed  in  living 
figures.  They  cannot  understand  the  thing  signified 
unless  they  first  know  the  facts  through  which  it  is 


ZOOLOGY.  85 

signified.  Nature,  like  the  Gospels,  speaks  in  para- 
bles to  those  who  cannot  understand  the  truth  in  other 
forms  ;  and  children  are  pleased  and  instructed  when 
allowed  and  encouraged  to  read  those  parables  for 
themselves  Nor  is  there  any  purer,  or  more  perman- 
ent source  of  happiness  and  of  wisdom  that  can  be 
opened  to  them,  than  this  habit  of  reverently  reading 
for  themselves,  the  lessons  of  nature. 

The  principles  which  I  am  endeavoring  to  apply  in 
what  I  say  of  the  subprimary  and  primary  schools,  are 
easily  applied  to  the  whole  course  of  liberal  education; 
— by  liberal  education  I  mean  that  education  which 
fits  one  for  the  social  and  political  duties  of  a  free- 
man ;  without  rigorously  excluding  every  thing  that 
might  be  considered  as  professional  training.  For 
liberal  education,  the  course  of  physics  should,  in 
proportion  as  the  pupils  mind  enlarges,  deal  gradually 
more  with  general  laws,  and  less  with  the  details  by 
which  those  laws  are  established.  The  ability  and 
habit  of  patient  and  exact  observation  having  once  been 
gained,  then  the  wider  and  more  general  the  princi- 
ples which  you  give  your  pupil,  the  more  practically 
useful  will  your  teaching  be.  This  is  the  true  method 
of  the  Novum  Organum  ;  ascendendo  ad  axiomata,de- 
sccjidcndo  ad  opera.  Physics  and  Natural  History  were 
thirty  years  ago  unjustly  neglected  in  our  general 
education  ;  there  is  danger  to-day  lest,  in  the  reaction, 
they  are  allowed  to  claim  an  unjust  portion  of  atten- 
tion. They  belong,  as  means  of  liberal  education,  to 
the  schools  more  truly  than  to  the  colleges ;  in  the 
latter  their  place  is  rather  as  a  part  of  philosophy, 


86  TRUE    ORDER    OF    STUDIES. 

than  as  a  training  in  observation.  History,  literature, 
politics,  psychology  and  theology  are  the  more  appro- 
priate studies  for  a  collegiate  course. 

In  the  grammar  and  high  schools,  after  a  proper 
preparation  in  the  younger  grades,  we  can  readily  give 
as  much  of  the  mechanical  sciences,  and  sciences  of 
natural  history,  as  it  is  profitable  to  teach  to  those 
who  have  no  special  aptitude  for  the  studies.  I  ac- 
knowledge that  this  is  impossible  with  the  prepara- 
tion now  given  in  the  primary  and  subprimary 
schools  ;  and  that,  therefore,  a  part  of  the  collegiate 
course  is  necessarily  occupied  in  giving  instruction  in 
the  physical  sciences,  better  adapted  to  children  than 
to  youth.  The  preparation  of  such  excellent  text 
books  as  Guyot's  Earth  and  Man.  and  of  Agassiz  and 
Gould's  Zoology  is  thus  rendered  a  thankless  task ; 
these  books,  adapted  for  the  widest  usefulness  in  high 
schools,  are,  by  the  insufficient  preparation  of  the 
younger  scholars,  confined  to  a  few  of  the  most  ad- 
vanced institutions.  Within  a  fevv  years  past,  good 
text  books  have  been  prepared  in  Geography,  Botany, 
and  Zoology,  for  younger  children, — very  good,  if  they 
be  used,  as  some  of  the  best  were  meant  to  be,  by  the 
teacher  alone,  and  the  child  have  the  globe,  thejjlant 
and  the  animal  put  into  his  hands  for  study.  It  is 
absurd  to  attempt  to  teach  from  text  books  alone  ; 
and  in  the  most  modern  style  of  text  book,  each  sub- 
ject is  expanded  so  fully  that  the  child  who  studies 
his  school  text  books  has  no  time  left  in  which  to 
play,  much  less  any  time  to  study  nature  ;  and  the 
teacher  who  examines  the  pupil,  in   so  called  recita- 


ZOOLOGY,  87 

tions,  sufficiently  to  know  whether  it  has  studied  the 
whole  of  the  text  book,  has  no  time  left  in  which  to 
teach  anything. 

Changes  in  the  system  of  public  education  are 
usually  made  with  difficulty  ;  and  it  is,  doubtless,  well 
that  it  is  so  ;  since,  otherwise,  our  schools  would 
suffer,  even  more  than  at  present,  from  the  eccentri- 
cities and  errors  of  those  who  have  control  over  them. 
At  present,  the  legal  guardians  of  the  school,  the 
teachers,  the  scholars,  and  the  parents,  constitute 
four  classes,  who  resist  every  change,  whether  for 
better,  or  for  worse.  In  the  changes  which  I  liave 
been  advocating  now  for  thirty  years,  the  difficulty 
has  been  greater  from  the  fact  that  the  proposed 
alterations  require  an  alteration  from  the  very  begin- 
ing  of  the  course,  in  the  alphabet  school.  It  must  be 
confessed  that  my  scheme  of  high  school  instruction 
is  impracticable,  unless  the  pupils  have  been  from 
their  first  entrance  into  the  lowest  school,  trained  in 
habits  of  exact  observation,  and  rapid,  accurate  con- 
ception ;  and  taught  to  grasp  and  become  familiar 
with  the  results  of  sound  inductive  reasonings. 

So  far  from  this  being  the  case  in  ordinary  schools, 
we  might  more  truly  say  that  there  the  child  is  taught 
to  neglect  observation,  to  withdraw  his  mind  from  any 
healthy  interest  in  things  around  him,  to  value 
words  above  ideas,  to  repeat  phrases  to  which  he 
attaches  no  meaning,  to  adopt  the  results  of  hasty  and 
unsound  speculations.  Even  to  the  present  day  there 
are  very  few  schools  into  which   minerals,   plants,  or 


83  TRUE    ORDER    OF    STUDIES. 

animals  are  ever  brought  for  examination  ;  very  few 
teachers  who  themselves  know  the  difference  between 
a  moss  and  a  lichen,  a  bug  and  a  beetle,  a  moth  and  a 
butterfly,  or  who  would  not  reprove  a  child  for  bringing 
such  things  into  the  school  room  ;  in  nearly  all  schools 
the  pupil  is  taught  to  spell,  that  is  to  deny  the  truth 
of  his  own  sense  of  hearing  ;  and  this  is  done  so  per- 
tinaciously and  thoroughly  that  by  the  time  that  he 
leaves    the  high  school  he   hears  in  a   spoken  word 
sounds  that  are  not  there,  and  fails  to  hear  sounds 
that  are.     Drawing  has  been  largely  introduced  into 
the  schools  within  a  few  years,  but  not  for  the  reasons 
for  which  the  soundest  writers    on    education    have 
urged  it.       Commercial,  financial  reasons  have  led  to 
its  introduction  ;  in  a  form  which,  however  valuable, 
fails  to  give  it  its  highest  value  ;  it  is  drawing  from  a 
copy,  and   thus   but  feebly   exercises   the   observing 
powers  ;  or  it  is  inventive  drawing,  which  does  not 
develop  the  observing  powers  at  all.     Arithmetic  was 
after  a  long  struggle  against  the  tyranny  of  grammar 
introduced  into  schools,  and  has  now  become  a  king 
stork  more  intolerable  than  a  king  log.     It  owes  its 
popularity  to  the  obviousness  of  its  practical  applica- 
tions ;  but  it  is  pursued,  at  the  present  day,  princi- 
pally as  a  premature  drill  of  the  reason,  and  thus  the 
practical  end  of  learning  to  cypher  is  lost,  with  no 
counter-balancing  advantage  ;  and  the  study  occupies, 
in  the  ordinary  school,  at   least  double    the  time  in 
which  it  could  be  thoroughly  acquired,  if  it  weiemade 
first  a  matter  of  direct  sight,  secondly,  practised  as  an 


ZOOLOGY,  89 

art,  and  lastly  studied  as  a  science.  Geography  is 
the  only  study  in  the  ordinary  school  which  can  be 
called  a  science  of  observation,  and  even  that  is  taught 
as  a  matter  of  imagination,  the  things  seen  in  the 
ordinary  school  being  words  and  maps,  not  the  real 
earth  and  sky.  All  these  points  show  that  the  ordi- 
nary schooling  in  the  primary  school  gives  no  sort  of 
adequate  preparation  for  scientific  instruction  in  the 
high  and  grammar  schools. 

For  this  reason,  I  occupy  myself  more  especially 
m  indicating  what  I  conceive  to  be  the  true  time  and 
mode  of  beginning  each  branch  of  study.  I  pass  by 
the  studies  of  the  high  school  and  the  college,  not  from 
want  of  interest  in  them,  but  from  a  conviction  that  he 
who  would  produce  the  highest  educational  effect  must 
begin  with  the  youngest  pupils.  Each  days  mental 
state  depends,  in  part,  upon  our  previous  education,  the 
mental  development  of  to-day,  depends  in  part  upon 
the  education  of  yesterday  ;  and  that  of  yesterday, 
upon  that  of  the  day  before.  We  must  acknowledge 
this,  even  if  we  do  not,  with  Herbert  Spencer,  con- 
sider our  mental  development  as  the  culminating 
result  of  the  education  of  our  ancestors  through 
countless  generations.  Moreover  we  must  acknowl- 
edge that  a  stronger  impression  is  made  upon  a  young 
person  than  upon  an  old  ;  that,  although  one  is  never 
too  old  to  learn,  he  soon  becomes  too  old  to  learn 
easily.  I  simply  would  express  my  earnest  conviction 
that  the  best  time  for  the  cultivation  of  geometric 
ability,  and  the  power  of  observation,  is  in  very  early 


go  TRUE    ORDER    OF    STUDIES. 

childhood  ;  that  we  do  a  grievous  wrong  to  our  young 
children  by  drawing  their  attention  from  objects  of 
natural  history,  and  things  which  they  can  handle,  and 
by  forcing  them  to  pore  over  a  false  alphabet,  and 
Arabic  figures  which  have  no  interest  for  them. 


GEOLOGY.  91 


CHAPTER  XII. 

GEOLOGY. 

WHEN  the  pupil  has  some  clear  ideas  concern- 
ing the  present  condition  of  the  earth  and 
ihe  solar  system,  his  natural  instincts  will  lead  him  to 
inquire  concerning  the  ancient  history  of  these  bodies. 
The  majority  of  school-houses  in  the  United  States 
are  built  upon  the  drift,  or  upon  alluvial  deposits.  A 
child  of  any  activity  of  mind,  brought  up  upon  the 
drift,  will  at  a  very  early  period  perceive  that  the  peb- 
bles around  him  are  fragments  of  rock,  rounded  and 
worn  smooth,  by  some,  to  him,  unknown  agency.  The 
boys  with  whom  I  played  in  my  childhood  were  con- 
tinually speculating  concerning  the  rounded  pebbles 
of  silex  and  jasper  scattered  over  the  red  sandstone  of 
Central  New  Jersey.  The  children  of  Norfolk  county, 
Massachusetts  are  forever  questioning  concerning  the 
great  lumps  of  pudding  stone  scattered  over  the 
ground.  In  Ohio  and  other  Western  States,  the 
children,  playing  in  the  streets  of  the  cities,  stop  to 
ponder  over  the  fossil  imbedded  in  the  limestone  slabs 
with  which  the  sidewalks  arc  paved. 

It  is  only  within  forty  years  that  any  very  satis- 
factory answer  could  be  given  by  teachers  or  parents, 
to    children    questioning    them   upon    these    things. 


92  TRUE    ORDER    OF    STUDIES. 

When  Agassiz  first  gave  a  rational  answer  to  inquiries 
concerning  the  drift,  ev^en  the  most  learned  geologists 
refused  to  accept  it,  and  clung  to  their  inadequate,  and 
confused  notions  of  water  and  floating  ice  ;  which  the 
healthy  intellectual  instincts  of  children  rejected  as 
wholly  inadequate  to  explain  the  problem.  But  twenty 
years  of  battle  for  the  obvious  truth  was  at  length  suc- 
cessful, and  the  existence  of  a  glacial  period,  as  the 
immediate  precursor  of  the  present  epoch,  is  so  well 
established  now,  that  there  need  be  no  hesitation  in 
giving  it  to  children  as  a  fact.  In  like  manner  the 
older  truths,  of  the  long  succession  of  preliminary 
ages,  and  of  the  deposits  of  mud,  afterwards  hardened 
into  stone,  around  animals  which  have  long  since 
perished  from  the  earth,  may  safely  be  given  as  facts, 
more  interesting  than  any  fictions — 

Through  the  window  we  are  peering 

Into  ancient  realms  o£  shade  ; 
Lo  !  instead  of  ghosts  appearing, 

Creatures,  like  the  present  made. 

None  of  Pluto's  fabled  terrors, 

Neither  Sphynx,  nor  Harpies  dire  ; 

Nor  Chimaeras,  (fearful  errors  !) 
Lick  up  hell-born  flames  of  fire. 

No  !  within  these  quiet  places, 

Daemons  foul  no  vigils  keep; 
But  a  thousand  dreaming  races 

Lie  in  an  eternal  sleep. 

In  old  time,  the  Sun  arisen 

Made,  for  them,  the  world  shine  bright; 

Now  the  rocks  their  forms  emprison. 
Closed  in  everlasting  night. 


GEOLOGY.  93 

So  sings  Oswald  Heer ;  and  the  child  is  as  much 
entranced  with  the  new  stories  as  with  the  old.  Only 
let  due  care  be  taken  to  distinguish  as  accurately  be- 
tween facts  and  imagination  in  the  new  forms  as  in  the 
old.  In  Darwin's  "  Voyage  of  the  Beagle  "  he  closes 
with  an  emphatic  warning,  which,  it  seems  to  me,  he 
himself,  thirty  years  afterwards,  entirely  disregarded  ; 
an  emphatic  warning  against  the  temptation,  which 
constantly  assails  the  student  of  geology,  to  bridge 
over  the  gaps  of  knowledge  by  loose  and  unfounded 
speculations.  His  warning  needs  to  be  earnestly  re- 
peated at  the  present  moment,  to  the  teachers  of  the 
young  ;  since  his  enthusiastic  followers  are  constantly 
assuming  that  his  recent  speculations  are  established 
inductions  and  have  the  authority  of  science.  There 
are  facts  enough  established  in  this  science, — the 
origin  of  fossils,  the  formation  of  ancient  and  modern 
rocks,  the  origin  of  the  drift,  and  of  alluvial  deposits, 
the  nature  of  the  various  coals,  and  coal  oils,  the  for- 
mation of  continents,  the  direction  of  the  great  moun- 
tain chains  and  coast  lines,  and  its  connection  with 
the  obliquity  of  the  Ecliptic,  the  duration  of  the  pre- 
sent epoch, — to  give  to  the  child  as  incidental  oppor- 
tunities occur  ;  facts  which  will  enlarge  the  scope  of 
his  thought  and  imagination,  and  prepare  him  to  re- 
ceive new  truths  as  they  may  be  presented  to  him  in 
after  life. 


94  TRUE   ORDER   OF   STUDIES. 


CHAPTER  XIII. 

COMMODITY. 

OUR  third  great  division  of  human  science  in- 
cludes all  that  is  historical, — -all  that  relates  to 
man's  action,  what  he  has  said  and  done.  This  di- 
vision, as  we  have  already  said  (p.  1 8  )  may  be  roughly 
divided  in  four  groups  ;  the  first  treating  of  man's  use 
of  nature  for  commodity  ;  that  is,  for  purposes  of  agri- 
culture, manufactures  or  commerce.  The  second 
embraces  the  fine  arts  ;  the  third,  language  ;  and  the 
fourth,  social  life,  custom,  and  law.  The  reasons  for 
this  subdivision,  and  for  the  order  in  which  the  groups 
are  arranged,  will  be  evident  on  a  moment's  thought. 
The  use  of  the  world  for  our  bodily  needs  is  first  in 
order  of  time  and  of  simplicity  ;  the  earliest  knowledge 
that  a  child  has  of  the  work  of  man,  as  distinguished 
from  the  work  of  nature,  consists  in  knowing  to  what 
uses  man  puts  the  material  things  furnished  by  nature. 
We  must,  however,  confess  that  this  precedence  is 
logical  rather  than  chronological  ;  since  the  child  has 
been  in  the  world  but  a  year  or  two  before  it  uses 
dolls,  and  pictures,  that  is,  works  of  art,  as  naturally  as 
it  does  food  or  clothing.  The  invention  of  language 
is  more  manifestly  subsequent  to  the  use  of  material 
things  ;  and  it  is  also  manifest  that  the  ability  to  com- 


COMMODITY.  95 

municate  ideas  by  language  must  precede  every  at- 
tempt at  social  order  or  law. 

Without  historical  knowledge,  a  child  would  grow 
up  a  barbarian.  The  educated  man,  and  the  highly 
civilized  nation,  are  chiefly  distinguished  by  their  ad- 
ding to  the  inheritance  received  from  their  fathers,  a 
knowledge  of  what  that  inheritance  is,  and  how  it  was 
gained  by  those  who  have  transmitted  it  down  the 
ages.  Yet  the  history  of  manufactures,  commerce 
and  agriculture  is  seldom  taught  in  the  schools.  Books 
on  trade,  on  commerce,  on  the  economy  of  manufac- 
tures, although  recommended  by  many  of  the  best 
writers  on  education,  have  never  enjoyed  a  wide  popu- 
larity. The  great  obstacle  here,  as  in  all  the  historical 
branches,  consists  in  the  multiplicity  of  details  which 
seems  to  be  involved.  It  is  with  difficulty  that  the 
good  teacher  finds  general  principles  cover  the  facts 
of  agriculture,  manufactures  and  commerce  ;  and  he 
knows  that  a  knowledge  of  general  principles  is  the 
only  knowledge  practically  useful  in  the  highest  sense. 
Instruction  upon  these  matters  remains,  therefore,  at 
present,  almost  wholly  "  incidental  "  ;  and  is  received 
in  the  family  more  than  at  school.  A  very  young 
child,  is,  however,  greatly  interested  in,  and  benefited 
by,  even  such  instruction.  In  the  cities,  let  him  see 
the  planting  of  seeds  and  bulbs  in  pots,  and  watch  the 
growth  of  the  plants  in  the  school-room  window ;  in 
the  country  let  the  same  lesson  be  given  in  a  bed  in 
the  school  yard.  The  processes  of  planting,  watering, 
weeding,  loosening  the  surface,  manuring,  (in  the  city 
with    nitrate    of   ammonia),  pruning,    collecting   the 


96  TRUE    ORDER    OF    STUDIES. 

seed,  etc.,  will  furnish  abundant  opportunities  for  the 
most  valuable  incidental  instruction  ;  concerning  the 
dependence  of  man  and  animals  upon  plants  ;  the  uses 
of  the  atmosphere  and  rains  ;  the  right  of  man  to  re- 
move plants  when  out  of  place  ;  the  ethical  objection 
to  a  needless  destruction  of  them  ;  the  nature  of  the 
dew,  and  of  evaporation  ;  the  arrangement  of  the  leaves 
to  catch  the  light,  the  necessity  of  light  for  green- 
leaved  plants  ;  the  adaptation  of  different  plants  to 
different  climates  and  situations  ;  the  various  parts  of 
plants  used  by  man  ;  the  modes  of  increasing  the 
yield,  and  of  arresting  the  deterioration  of  soils. 

Again,  every  one  of  the  articles  in  household  use 
may  furnish  lessons  concerning  the  mode  in  which 
men  bring  the  raw  materials  into  subservience  to 
man's  needs.  The  processes  of  grinding  and  bolting 
wheat ;  of  fermenting  and  baking  bread  ;  of  planting, 
tending,  gathering,  cleaning,  carding,  spinning,  weav- 
ing, bleaching,  dyeing  or  printing  cotton  ;  of  tending 
sheep  ;  of  shearing  and  cleansing  wool ;  of  spinning, 
dyeing  and  weaving  yarn  into  the  various  kinds  of  cloth 
and  carpeting ;  of  tanning  leather  and  making  boots 
and  shoes  ;  of  manufacturing  glass ;  of  digging  and 
smelting  ores  and  working  metals  ; — in  short,  of  pro- 
ducing from  the  raw  material  any  one  of  these  articles 
which  the  pupil  daily  sees  and  handles, — will  furnish 
subjects  for  valuable  instruction  ;  even  if  the  details 
are  forgotten,  the  general  impression  remains,  of  the 
nmltiplicity  of  human  industries,  and  the  utter  lack  of 
excuse  for  any  man  being  a  drone  in  this  busy  hive, 
ihe  earth. 


COMMODITY.  97 

If  the  teacher  is  ignorant  concerning  such  matters, 
the  school  ought  to  be  furnished  with  reference  books, 
Hke  the  Penny  Encyclopedia,  or  Chambers',  or  the 
American  Encyclopedia,  or  at  least  with  smaller  books 
prepared  expressly  for  the  young.  Undoubtedly  the 
best  mode  of  instructing  a  child  concerning  any  of  the 
operations  of  the  useful  arts,  is  to  allow  him  to  see  the 
process  going  on  ;  and,  whenever  practicable,  this 
course  should  be  adopted.  It  is  not,  however,  always 
convenient  for  a  manufacturer  to  be  interrupted  by 
visitors ;  and  in  some  places  it  would  be  dangerous  to 
allow  children  to  pass  among  machinery  arranged  for 
work,  and  not  for  show.  But  advantage  should  be 
taken  of  those  places  where  work  can  be  seen  without 
interruption  to  the  workmen  ;  and  especially  of  indus- 
trial exhibitions,  and  mechanics'  fairs. 

Beside  the  enlargement  of  mind,  the  extension  of 
the  circle  of  ideas,  the  increase  in  the  power  of  con- 
ception,— which  a  child  must  gain  from  the  examina- 
tion of  agricultural  tools,  labor-saving  machinery,  and 
processes  of  manufacture — he  will  be  likely  to  choose 
his  occupation  in  life  more  intelligently,  and  with  a 
more  just  reference  to  his  own  powers.  The  attrac- 
tion which  figured  so  prominently  in  the  socialist's 
theories,  cannot  have  fair  play  and  bring  the  young 
man  into  his  appropriate  sphere  of  labor,  if  this  op- 
portunity has  not  been  afforded  him  of  knowing  what 
spheres  are  open  to  him.  A  history  .of  inventions,  a 
book  containing  the  first  rudiments  of  agriculture, 
"  Babbage's  Economy  of  Manufactures,"  and  similar 
works  oujrht  to  be  embraced  in  the  child's  reading;. 


98  TRUE    ORDER    OF    STUDIES. 

Miss  Edgevvorth's  "  Harry  and  Lucy  "  answers  toler- 
ably in  school  use  ;  also,  the  "  Evenings  at  Home  "  ; 
but  I  am  not  acquainted  with  any  modern  imitations 
that  handle  these  subjects  well,  although  there  are 
several  treatises  which  are  better  than  nothing. 


ARi:  99 


CHAPTER   XIV. 

ART. 

THE  moment  that  man's  bodily  needs  are  satisfied, 
he  begins  to  express  his  feehngs  in  art.  Music, 
and  dancing,  sculpture  and  painting,  are  as  natural  to 
man  as  eating  and  drinking.  The  child  of  two  years 
old  makes  anything  into  a  doll,  and  recognizes  in  the 
rudest  picture  the  designed  resemblance  to  man  or 
dog,  tree  or  house.  Even  the  likeness  to  individuals, 
in  the  photograph,  is  thus  early  recognized.  At  three 
years  old,  the  child  begins  to  sing ;  and  readily 
catches  a  melody. 

In  the  kindergarten,  the  child  begins  at  an  early 
age  to  model  in  clay  ;  and  it  would  be  a  great  boon 
to  our  children  could  something  cleaner  than  clay  be 
invented,  sufficiently  cheap  to  allow  this  feature  of 
Frobel's  system  to  be  adopted  in  all  the  public  pri- 
mary schools. 

Drawing  has  of  late  years  received  increased  at- 
tention, and  Walter  Smith's  system  of  instruction 
seems  to  leave  nothing  to  be  desired  as  an  introduc- 
tion to  drawing  as  an  industrial  art.  For  the  pur- 
poses of  intellectual  and  artistic  education  it  needs, 
however,    to    be    supplemented    by    drawing    from 


TOO  TRUE    GREET?    OF    STUDIES. 

nature  ;  else  it  fails  to  exercise  its  peculiar  power  as 
a  stimulus  to  observation,  to  purity  of  tasie,  and  to 
appreciation  of  natural  beauty.  The  leaves  brought 
in  for  botanical  study,  or  even  the  pressed  leaves, 
kept  in  the  school-house  for  types  of  reference,  make 
excellent  copies  for  the  young  draughtsman  ;  as  do 
also  the  shells  and  msects,  which  ought  to  make  part 
of  the  common  school  furniture.  The  young  ob- 
ser\^er  will  not  see  the  peculiarities  of  the  natural 
object,  nor  its  graceful  beauty,  until  he  attempts  to 
copy  it  with  the  pencil.  I  have  alluded  to  Agassiz's 
saying  that  a  lead  pencil  is  an  excellent  microscope  ; 
Professor  E.  S.  Morse,  in  his  admirable  First  Book  of 
Zoology,  expands  the  idea  by  saying  that  "  a  specimen 
or  figure  may  oftentimes  be  carefully  studied,  and  yet 
only  an  imperfect  idea  be  formed  of  it ;  but  when  it 
has  once  been  copied,  the  new  points  gained  repay  all 
the  trouble  spent  in  the  task." 

The  first  lessons  must,  of  course,  be  in  copying 
the  simplest  forms  of  leaves  and  shells  ;  afterwards, 
the  more  complex  forms  ;  then  the  insects.  When 
considerable  facility  in  drawing  has  been  obtained, 
and  the  power  of  accurate  observation  gained, — 
greater  quickness  of  perception  may  be  formed  by  a 
process  similar  to  that  recommended  in  Arithmetic 
and  Geometry.  A  new  leaf,  or  shell,  may  be  ex- 
posed to  full  view  for  a  short  time,  shorter  in  propor- 
tion to  the  proficiency  of  the  class,  and  then  covered, 
while  the  class  copy  the  outline  from  memory. 
Drawing  thus  from  nature,  and  especially  from  fresh, 


ART,  lOI 

living  plants  and  animals,  stimulates  the  pupil's 
powers  of  observation  and  conception  to  vastly  higher 
activity,  than  drawing  from  copies  ;  giving  him 
greater  pleasure,  and  greater  increase  of  power.  By 
this  means,  progressive  courses  in  drawing  from  copy, 
and  in  invention  from  the  suggestions  of  nature,  will 
be  made  much  more  profitable. 

The  real  order  of  procedure  in  education  has 
never  been  so  much  neglected  in  music,  as  in  the 
other  arts  ;  yet  great  advances  have  been  made  within 
the  past  twenty  years,  and  the  most  admirable  results 
obtained.  Singing  has  been  very  extensively  intro- 
duced into  public  schools  ;  and,  although  in  many 
places  a  mischief  has  been  done  by  requiring  the 
children  to  scream,  and  by  misleading  their  ears  with 
a  pianoforte,  always  out  of  tune,  the  mischief  has  been 
overbalanced  by  the  good.  In  other  places,  and 
especially  in  Boston,  the  advantages  have  been  gained 
almost  without  a  mixture  of  evil.  The  pupils  are 
taught  to  depend  upon  their  own  ears,  to  keep  the 
tones  pure,  soft  and  natural,  to  read  the  musical  staff 
as  easily  as  a  printed  page,  and  to  give  the  absolute 
pitch  as  easily  as  they  give  the  true  vowel  or  conso- 
nant sounds  of  the  language.  The  selections  also  in 
the  Readers  aje  made  with  correct  taste,  from  stan- 
dard authors.  Were  such  instruction  as  that  given 
by  Luther  W.  Mason  in  Boston,  given  in  the  schools 
generally,  it  would  be  impossible  to  circulate  the 
books  of  psalmody  and  Sunday  School  hymns  which 
are  now  by  their  popularity  a  disgrace  to  our  country, 
and  to  our  race, — from  the  flatness  of  their  words  and 


102  TRUE  ORDER  OF  STUDIES. 

their  music.  The  great  end  of  teaching  art  in  the 
public  schools  is  not  to  create  artists,  but  to  give  all 
the  pupils  more  enjoyment  in  a  true  appreciation  of 
art  and  of  nature. 


LANGUAGE.  IO3 


CHAPTER  XV. 

LANGUAGE. 

THE  Study  of  the  very  extensive  group  of  histori- 
cal sciences  included  under  the  name  of  lan- 
guage, logically  follows  the  study  of  labor  and  of  art ; 
we  must  know  things  before  we  can  talk  about  them  ; 
and  language  logically  precedes  the  study  of  law  ;  we 
must  communicate  our  ideas  before  we  seek  to  enforce 
them.  But  practically,  in  chronological  order,  the  study 
of  language  begins  at  the  moment  after  birth,  and 
by  the  time  that  a  child  enters  the  public  school,  he 
can  talk  somewhat  fluently.  The  first  point  of  in- 
struction will  naturally  be  to  teach  him  to  read  and 
to  write  the  language  which  he  has  already  learned 
to  speak. 

The  words  which  he  uses  are  in  his  mind  signs  of 
things,  and  he  has  no  more  analysed  the  parts  of  a 
word  than  he  has  analysed  the  parts  of  the  thing  it 
stands  for.  At  first  this  is  the  best  method  of  intro- 
ducing him  to  the  printed  language,  not  to  its  letters, 
but  to  its  words  as  wholes.  As  when  you  hold  up  the 
picture  of  a  dog,  and  ask  what  it  is,  you  do  not  wish 
him  to  say,  "  It  is  the  picture  of  a  dog,"  nor  that  "  it 
is  one  side  of  the  head,  one  hind  leg,  and  both  fore 
legs  of  a  dog,"  but  when  he  sees  the  picture,  you  wish 


I04  TRUE    ORDER    OF    STUDIES. 

him  to  say,  it  is  a  dog  ;  so  when  he  sees  the  printed 
word,  you  wish  him  to  say,  not  dee  oh  jee,  but  dog. 
Teach  him  thus  to  read  very  simple  sentences,  con- 
taining only  the  most  common  word.s,  by  pronouncing 
at  sight  each  word,  and  continue  at  this  for  some 
months,  until  the  chnd  lecognizes  instantly,  at  sight, 
about  a  hundred  words  of  our  language,  such  as  are 
used  in  his  primer,  and  have  been  copied  in  writing 
text  upon  the  blackboard. 

When  this  point  is  thus  practically  established  in 
his  mind,  that  written  and  prmted  words  are  individ- 
ual pictures  of  spoken  words,  we  may  begin  the  an- 
alysis of  the  words  into  their  elements.  ,If  now  the 
primer  has  been  in  the  Cincinnati  Phonotype,  your 
task  is  delightfully  easy  ;  if  in  Dr.  Leigh's  Pronounc- 
ing Orthography,  it  will  present  some  difificulty  ;  and 
if  you  have  only  had  the  ordinary  type  the  difficulties 
will  be  greater  than  in  any  part  of  the  whole  course 
of  education. 

The  first  step,  in  cither  of  the  three  cases,  is  how- 
ever the  same,  and  is  easy  ;  the  child  must  be  taught 
to  analyze  by  his  ear,  the  spoken  word,  which  he  can 
do  by  simply  pronouncing  it  vety  slowly.  He  will 
soon  discover  that  all  the  sounds  of  our  English 
speech  can  be  divided  into  about  forty  classes,  each 
one  of  which  may  be  called  an  elementary  sound- 
This  sounds  learned,  and  beyond  a  child's  reach  ;  but 
practically  the  best  way  to  teach  a  child  of  three 
years  old,  to  pronounce  a  difficult  word,  i-s  to  make 
him  pronounce  the  phonic  elements  of  it  separately 
and  successively,  and  then  blend  them.     This  is  pho- 


LANGUAGE.  IO5 

netic  spelling,  and  a  child  of  five  or  six  years  old  will- 
grow  enthusiastic  in  such  spelling,  as  an  amusement, 
before  he  knows  a  single  letter  of  his  alphabet. 

When  the  pupil  can  with  facility  analyze  the 
spoken  words  into  their  phonic  elements,  he  must  be 
taught  that  alphabetic  writing  originated  in  an  attempt 
to  represent  each  element  by  a  letter.  With  the  Cin- 
cinnati alphabet  this  is  done  for  English  ;  and  the 
child  has  but  to  learn  the  sound  of  each  letter,  in 
order  to  read.  With  Dr.  Leigh's  type,  or  with  com- 
mon type,  the  child  must  now  be  taught  that  tliis 
original  attempt  of  alphabetic  writing  is  very  imper- 
fectly carried  out  in  English  ;  that  he  will  find  each 
letter  has  various  sounds,  or  is  sometimes  silent  ;  and 
that  each  sound  has  various  modes  of  being  repre- 
sented in  words.  Great  care  must  be  taken  not  to 
let  him  use,  or  even  know,  at  first,  the  names  of  the 
English  letters.  For  instance,  A  must  be  named  as 
it  is  pronounced  in  at  ;  B  must  be  named  simply  as 
pronounced  in  hub,  whispering  inaudibly  the  hu,  and 
pronouncing  aloud  the  mere  end  of  the  word  ;  C  as 
in  the  end  of  music  ;  D  as  at  the  end  of  had  ;  G  as  at 
the  end  of  hag,  &c.  Not  until  the  child  is  perfectly 
familiar,  by  many  months  practice,  with  the  fact  that 
H  signifies  a  slightly  roughened  breathing,  ought  it 
to  be  allowed  to  call  it  aitch. 

Unfortunately  the  English  alphabet  contains  but 
twenty-six  letters,  three  of  which,  c,  q,  and  x,  are 
superfluous  ;  while  the  sounds  which  ought  to  be 
represented  are  from  34  to  40.  And  in  addition  to 
this  necessity  for  using  the  same  letter  to   represent 

r* 


I06  TRUE  ORDER  OF  STUDIES. 

different  sounds,  (as  for  example,  t  in  bat,  bath,  bathe) 
we  add  the  unnecessary  use  of  various  letters  and 
combinations  to  represent  the  same  sound,  (as  for  ex- 
ample, nay,  neigh,  nail,  nation,  they,  fete,  and  other 
ways  of  writing  the  sound  a).  Some  writers  have 
maintained  that  there  are  but  trifling  exceptions,  and 
that  the  mass  of  our  language  is  truly  phonetic.  But 
this  is  a  mistaken  view ;  the  exceptional  words  occur 
so  frequently  that  not  only  is  a  child  unable  to  pro- 
nounce a  new  word  by  the  aid  of  his  alphabet,  but  no 
scholar  of  whatever  ability  can  tell  the  pronunciation 
of  an  English  word,  which  he  has  never  chanced  to 
hear,  or  to  see  printed  with  diacritic  signs.  It  may 
therefore  be  justly  said,  that  English  is,  like  Chinese, 
not  alphabetic  in  its  dress,  but  logographic  ;  and  there 
is  no  man  living,  in  England  or  America,  who  has 
learned,  or  can  learn  to  read  it  ;  that  is  to  pronounce 
anything  and  everything  written  in  it. 

For  this  reason  learning  to  read,  being  the  attempt 
to  accomplish  an  impossible  thing,  is  the  most  diffi- 
cult task  undertaken  by  an  English  child.  A  tough 
constitution  resists  a  great  deal  of  hardship  and 
abuse  ;  a  vigorous  intellect  frequently  survives  the 
labor  of  learning  to  spell  in  the  ordinary  mode.  A 
man  who  has  lived  through  a  course  of  bad  diet,  and 
inattention  to  the  laws  of  health,  is  apt  to  regard  at- 
tention to  such  matters  as  a  mark  of  effeminacy  ;  and, 
in  like  manner,  those  whose  love  of  literature  has  not 
been  quenched,  and  whose  power  to  see  truth  has  not 
been  wholly  blinded,  by  the  ordinary  mode  of  learning 
tJ  read,  suppose  that  there  is  no  urgent  need  for  im- 


LANGUAGE.  IO7 

provemcnt.  He  who  will  reflect,  however,  seriously, 
upon  the  absurdities  of  English  orthography,  and 
upon  the  gravity,  with  which  those  absurdities  are 
usually  introduced  to  the  child  as  reasonable  things, 
must  perceive  that  such  instruction  has  an  injurious 
effect  upon  the  child's  mental  powers,  and  upon  his 
love  of  truth.  The  boy  may  survive  it  ;  as  he  sur- 
vived in  olden  days  compression  of  swathing  bands, 
drenching  with  herb-teas,  and  drugging  with  cordials  ; 
I  will  even  allow  that,  in  the  case  of  great  native 
vigor  of  mind,  the  injurious  effect  may  be  small :  but 
it  is  always  pernicious  ;  and  in  the  case  of  persons  of 
small  intellectual  ability,  disastrous.  The  child  is  told 
to  spell  a  word,  and  then  expected  to  pronounce  it ; 
as  though  the  spelling  were  a  guide  to  the  pronuncia- 
tion. I  remember  hearing  a  schoolfellow  hesitate 
when  he  came  to  the  word  "  business."  Spell  it ! 
said  the  teacher.  Be  you  ess  eye  n  e  ess, — double 
ess,  replied  the  boy.  Well !  and  what  does  that  spell  ? 
asked  the  teacher.  As  he  paused  for  a  reply  to  this 
unanswerable  question,  he  espied  a  larger  boy  doing 
something  wrong,  and  looking  sternly  at  him,  uttered 
his  name,  in  tones  of  reproof, — ChristopJier  Frazcr  ! 
The  little  fellow  thought  this  was  the  pronunciation 
of  his  "be  you  ess  eye,  &c.,"  and  meekly  repeated, 
Christopher  Frazer.  We  laughed, — and  yet  that 
jumble  of  the  names  of  the  letters  sounds  as  much 
like  Christopher  Frazer  as  it  docs  like  business. 

Even  if  it  be  not  desirable  to  change  the  printed 
form  of  our  language,  for  ordinary  purposes  in  books 
and  newspapers ;    it  is  extremely  desirable   that  the 

5* 


I08  TRUE  ORDER  OF  STUDIES. 

books  for  the  first  two  or  three  years  of  school  Hfe 
should  be  in  phonetic  print.  The  saving  of  time  thus 
effected  for  the  child,  if  the  Cincinnati  phonotype  be 
used,  has  been  experimentally  demonstrated  to  be  more 
than  a  year ;  and  with  Leigh's  type  more  than  six 
months  ;  but  the  saving  of  time,  although  very  valu- 
able as  giving  more  opportunity  for  geometrical  plays 
and  puzzles,  and  for  the  examination  of  objects  of 
natural  history,  is  not  worth  so  much,  as  the  increased 
happiness  of  school  life,  the  increased  sense  of  truth- 
fulness, the  increased  accuracy  of  ear,  and  spirit  of 
general  accuracy,  produced  by  it.  The  objection, 
made  by  those  who  have  not  tried  the  experiment,  of 
the  difficulty  of  transition  from  phonotype  to  common 
print,  is  of  no  weight.  The  pupil  who  reads  phono- 
type fluently^  can  in  one  fortnight,  without  appreci- 
able labor,  learn  to  read  common  print;  as  well  as  it 
is  possible  for  any  human  being  to  do  what  cannot  be 
done. 

The  child  who  learns  to  read  in  phonotype,  will 
learn  common  orthography  more  rapidly,  because  he 
perceives  more  clearly  its  oddities  and  anomalies ; 
and  that  fixes  them  on  his  memory.  Experiments  in 
Waltham  upon  many  hundreds  of  pupils,  continued 
through  a  series  of  six  or  seven  years,  showed  that 
those  who  had  learned  phonotype,  or  even  phono- 
graphy, were  better  in  spelling  than  other  scholars. 
Bad  spelling,  indeed,  usually  arises  from  an  attempt 
to  spell  phonetically  with  the  common  alphabet;  so 
that  we  might  say  that  the  cause  of  bad  spelling  is 
that  children  are  taught  to  spell.     For  this,  and  for 


LANGUAGE.  IO9 

Other  reasons  which  I  shall  presently  mention,  I  re- 
gard spelling  books  as  mischievous  ;  a  hindrance,  not 
a  help  to  learning.  A  child  accustomed  to  associate 
phonetic  values  only  with  a  peculiar  type,  and  know- 
ing that  the  common  spelling  is  traditional  and 
anomalous,  will  not  attempt  to  use  the  ordinary  alpha- 
bet phonetically,  and  will  thus  avoid  the  most  common 
source  of  errors.  The  use  of  a  phonotype,  or  even 
pronouncing  type,  has  also  the  advantage  of  giving 
unceasing  instruction  in  accuracy  of  enunciation  ;  and 
no  other  method  has  been  so  successful  in  removing 
from  a  school  provincialisms,  brogues,  and  vulgarities 
of  pronunciation. 

For  fixing  the  orthography  of  words  in  the  memory, 
no  practice  is  more  useful  than  constant  reading,  with 
frequent  writing  from  dictation  ;  but  the  latter  adjunct 
cannot  be  employed  at  the  earliest  age.  When  we 
have  a  phonotype  in  ordinary  use  in  our  literature,  the 
child  will  learn  the  current  hand  writing  at  the  same 
time  that  he  learns  print;  but  with  the  present 
heterotypy  (as  it  has  been  facetiously  called,)  we  must 
be  content  to  begin  writing  at  the  time  of  transition 
from  phonotypy  ;  when,  of  course,  the  progress  in 
writing  will  be  much  slower  than  in  reading. 

These  two  fundamental  arts  do  not  receive  in  our 
ordinary  schools  their  due  attention.  To  read,  to 
write  and  to  cypher  are  the  three  most  valuable 
accomplishments  taught  in  our  public  schools,  and 
should  take  precedence  in  importance  over  all  the  rest. 
Not  that  more  time  is  to  be  given  to  them  ;  too  much 
time  is  given  already  ;  what  is  needed  is  more  thought 


140  TRUE    ORDER   OF    STUDIES. 

and  attention,  good  judgment  and  good  taste.  What 
Luther  W.  Mason  has  done  with  music  in  the  Boston 
schools,  can  be  done  with  these  three  humbler  arts  in 
every  school.  All  art  is  imitative,  it  cannot  be  taught 
scientifically,  but  only  by  example.  Precepts,  direc- 
tions, principles,  are  of  value  only  to  the  student  who 
is  actually  trying  to  imitate  a  model.  To  learn  to 
cypher  the  child  must  see  the  teacher  perform  an 
arithmetical  operation ;  and  then  repeat  it  himself, 
until  it  is  familiar,  and  he  can  do  it  with  ease  ;  then, 
and  not  until  then,  is  the  time  to  explain  to  him  the 
reasons  for  what  he  has  done.  To  learn  to  read,  and 
write,  the  child  must  hear  the  teacher  read,  and  see 
the  teacher  write  ;  and  then  himself  go  over  the  sam€ 
sentence,  with  his  pencil,  and  with  his  lips,  until  he 
reads  it  readily.  It  is  idle  to  tell  a  little  child  to  let 
his  voice  fall  at  a  period,  to  stop  long  enough  to  count 
two  at  a  semicolon,  and  so  on.  Let  the  teacher  read 
the  sentence  in  easy  natural  tones,  in  such  wise  as  to 
bring  out  the  meaning ;  and  let  the  pupil  repeat  by 
ear. 

Pains  should  be  taken  from  the  very  beginning  to 
cultivate  pure  and  natural  intonation  ;  smooth  and 
melodious  sounds.  This  is  as  important  in  reading 
and  speaking  as  it  is  in  singing.  And  yet  I  have  been 
for  fifty  years  hearing  school  teachers  teach  their 
children  directly  the  reverse ;  constantly  saying, 
"speak  up,  let  out  your  voice,"  and  forcing  the  little 
things  to  shout,  and  scream,  in  harsh  unnatural  tones. 
Distinctness  of  articulation  can  be  best  gained  by  a 
careful  drill  on  the  phonic  elemenis  of  the  language, 


LANGUAGE.  I  I  I 

particularly  the  consonants  ;  and  sufficient  force  must 
of  course  be  given  to  make  the  reading  audible.  But 
a  boy  of  eight  or  ten  years  should  not  be  required  to 
speak  loud  enough  to  be  heard  by  a  school  of  150 
scholars ;  nor  should  a  child  of  any  age  be  allowed  to 
go  on  through  a  single  line  of  his  reading  book,  in  a 
strained,  unnatural  voice.  Few  scholars  of  American 
schools,  as  far  as  my  observation  goes,  are  at  present 
allowed  to  read  in  any  other  than  strained  tones. 

Nothing  but  practice  can  give  ease  and  facility  in 
an  art,  and  practice  takes  time.  This  is  a  second 
mode  in  which  the  spelling  book  is  injurious,  it  takes 
up  time  which  would  be  much  more  usefully  occupied 
in  reading.  It  is  reading  which  actually  does  the 
work,  with  which  the  spelling  book  has  usually  been 
credited.  When  a  scholar  has  learned  to  read  with 
perfect  facility,  so  that  the  printed  page  is  just  as  in- 
stantly intelligible  to  him  as  spoken  speech,  (and  in- 
deed a  good  reader  can  take  in  words  silently  from  a 
printed  page  more  than  thrice  as  fast  as  by  the  ear), 
then  the  forms  of  the  whole  words  of  the  language 
are  as  familiar  to  him  as  the  letters  of  the  alphabet, 
and  he  cannot  spell  a  word  in  any  other  way  than 
that  which  the  tyranny  of  lexicographers  and  proof- 
readers has  fastened  upon  him.  No  student  of  Greek, 
or  of  Latin,  or  of  a  modern  tongue,  uses  a  spelling 
book  in  acquiring  the  new  language  ;  yet  in  precise 
proportion  to  his  acquaintance  with  its  literature,  he 
can  spell  it.  It  is  so  with  the  vernacular  ;  and  all 
spelling  books  are  hindrances  to  learning  to  spell, 
they  take  up  time  which  ought  to  be  occupied  in 


112  TRUE  ORDER  OF  STUDIES. 

reading  ;  the  method  of  learning  what  we,  with  curious 
perverseness,  call  English  orthography. 

The  character  of  the  books  put  into  the  child's 
hands  is  an  important  matter.  By  the  modern 
method  of  using  in  schools  text  books  written  with 
profuse  explanations,  as  if  for  scholars  without  a 
teacher,  the  time  of  the  pupil  is  very  largely  occupied 
with  reading  his  text  books,  and  he  gets  little  time 
for  reading  literature.  The  reading  books  in  schools, 
which  were  formerly  made  by  compilation  of  classic 
authors,  are  now  too  largely  original  compositions  ; 
or  compilations  from  inferior  writers  ;  or  when  con- 
taining selections  from  classic  writers,  those  selections 
are  mangled  and  weakened.  These  inferior  books 
are  read  again  and  again  by  the  scholar.  When  at 
home,  many  children  have,  at  the  present  day,  a 
superabundance  of  books,  written  for  children,  and 
not  always  by  authors  of  the  highest  merit.  There  is 
danger  therefore,  real  and  imminent,  lest  our  children 
fail  to  enjoy  the  best  results  of  modern  thought ;  and 
fail  to  acquire  the  capacity  for  the  enjoyment ;  by  en- 
joyment I,  of  course,  do  not  refer  simply  to  the  pleas- 
ure received  from  art  and  literature  ;  but  also  to  the 
power  of  using  them  in  any  and  every  direction. 

A  plan  which  was  tried  in  Waltham,  to  obviate 
these  evils,  succeded  so  well  that  it  deserves  to  be 
more  widely  adopted.  First  selecting  the  briefest 
and  most  condensed  books  in  mathematics  and  the 
sciences,  (and  producing  thereby  better  results  in 
those  branches  also,)  we  next  provided,  at  the  expense 
of  the  town,  classic  authors    as  reading  books,  only 


LANGUAGE.  II3 

lending  them  to  the  scholars  while  in  actual  use. 
The  books  were  kept  in  good  order,  and  lasted  for 
many  successive  classes,  and  we  were  enabled  to  give 
the  children  a  greater  variety  than  usual.  For  the 
younger  scholars  we  had,  for  example,  Mrs.  Barbauld's 
Hymns  in  prose,  and  Maria  Edgeworth's  Early  Les- 
sons, while  in  the  High  School  we  had  Shakspeare, 
and  other  standard  writers,  English  and  American  ; 
introducing  some  books  of  a  scientific  character,  like 
Guyot's  Earth  and  Man. 

The  approach  to  ordinary  orthograpy  through 
phonetic  type,  (and  no  other  approach  ought  to  be 
permitted)  will  very  naturally  lead  to  questions  of 
etymology  :  which  will  interest  a  child  several  years 
before  he  is  old  enough  to  have  any  power  to  under- 
stand the  analysis  of  sentences,  or  any  form  of  syn- 
tax. Words  themselves  must  be  understood  before 
they  can  be  intelligently  classified.  When  a  word  is 
introduced  to  a  child  in  its  orthographic  dress  ;  and 
he  laughs,  as  well  he  may,  at  the  oddity  of  this  cos- 
tume ;  we  may  tell  him  of  its  gradual  growth  into  its 
present  form  ;  children's  and  foreigners'  mispronun- 
ciations will  illustrate  to  a  young  pupil  the  way  in 
which  words  may  change  ;  and  we  can  show  him  how 
the  silent  and  mispronounced  letters  in  a  word  are  a 
record  of  its  ancient  pronunciation,  or  of  its  deriva- 
tion, or  of  an  ancient  error  in  regard  to  its  supposed 
derivation.  This  will  lead  us  to  explain  to  him  the 
conventional  element  in  language  ;  that  usage  is  the 
law  and  rule  in  speech  ;  and  to  define  to  him  usage  as 
the  usage  of  a  majority  of  the  best  educated  ;   and  to 


114  TRUE  ORDER  OF  STUDIES. 

show  him  in  what  instances  a  usage  creeping  in 
ought  to  be  strenuously  resisted  by  the  educated 
classes.  When  a  geographical  name,  for  example,  is 
on  all  the  maps  and  charts,  it  is  an  offence  against 
morality,  akin  to  removing  a  neighbors  landmark,  to 
attempt  to  change  it.  Holmes'  Hole,  Roxbury,  Bangs 
Island,  Pequawket  Mountain,  are  geographical  names 
on  all  maps  and  charts  until  after  1850,  which  ought 
not  to  be  given  up  in  favor  of  the  much  inferior  sub- 
stitutes recently  invented.  Vineyard  Haven,  Boston 
Highlands,  Cushing's  Island,  Kiarsarge  Mountain. 
To  the  last  there  is  a  third  objection,  namely,  that  it 
sounds  so  much  like  Kearsarge  that  it  has  already 
produced  great  confusion  as  to  the  identity  of  two 
mountains,  fifty  miles  apart. 

We  may  then  go  further  back  with  our  pupil,  and 
show  him  that  a  part  of  our  language  is,  in  its  origin,  a 
natural  attempt  to  represent  the  thing  of  which  we 
speak.  We  may  show  him  how  a  sound  has,  in  a 
number  of  words,  the  same  meaning ;  the  compound 
element  sn,  for  example,  imitates  a  sneeze  and  seems 
to  call  attention  to  the  nose,  (in  which  word  the  ele- 
ments are  inverted)  ;  and  the  nasal  element  can  fre- 
quently be  detected  in  words  containing  this  sound. 
The  younger  classes  can  see  that  the  word  nose  can 
easily  be  introduced  into  the  definition  of  such  words 
as  sneeze,  snore,  snarl,  sneer,  snicker,  sniff,  snivel, 
snort,  snooze,  snout,  snub,  snuff,  snuffle  ;  and  even  of 
such  as  snail,  snake,  snap,  snare,  sneak,  snipe.  The 
older  classes  can  see  how  frequently  an  initial  th  points 
the  forefinger  ;  it  is  demonstrative, — as  in  this,  that, 


LANGUAGE.  1 1  5 

these,  those,  then,  there,  thither,  thence,  thus,  thou  ; 
while  the  initial  wh  is  relative,  that  is,  it  is  a  tJi  pre- 
ceded by  a  conjunction  ;  and  can  be  translated  by 
and  th  or  and  h.  Thus  :  "  I  saw  a  man  who,  etc.," 
is  equivalent  to  "I  saw  a  man  and  he."  A  similar 
force  is  in  what,  when,  where,  whence,  which,  whither, 
etc.  Still  older  classes  will  be  interested  to  see  that 
the  relative  is  an  interrogative  ;  a  question  always  im- 
plying a  previous  thinking,  with  which  the  conjunctive 
part  of  the  relative  connects  the  demonstrative  part. 
Such  plums  out  of  the  pudding  of  grammar,  will  awak- 
en, in  some  pupils,  a  taste  for  this  fascinating  study. 

The  forms  of  even  the  individual  letters  may  be 
made  the  occasion  of  incidental  instruction  upon  the 
origin  of  written  languages ;  the  probable  develop- 
ment of  Semitic  alphabets  from  phonetic  hierogly- 
phics ;  and  of  the  European  alphabets  from  those  of 
Phenicia.  If  such  instructions  fail  to  awaken  a 
scholarly  turn  of  mind,  and  to  lead  to  literary  taste, 
they  will  at  least  relieve  the  dryness  of  learning  to 
spell,  and  give  the  learner  some  glimpses  of  the  numer- 
ous and  subtle  ties  which  bind  us  to  all  the  generations 
which  have  preceded  us. 

The  study  of  grammar,  and  of  composition,  does 
not  belong  to  an  early  period  in  education.  Grammar 
is  the  study  of  a  maturer  mind,  and  may  be  wisely  de- 
ferred to  the  high  school ;  or  at  least  to  the  last  year 
of  the  grammar  school.  It  is  an  analysis  of  the  usages 
of  language,  and  requires  the  pupil  to  have  become 
familiar  with  those  usages. 

It  is  also  an  inversion  of  the  true  order  of  educa- 


Il6  TRUE  ORDER  OF  STUDIES. 

tion  to  give  a  child  an  abstract  theme  to  write  upon, 
before  he  is  old  enough  to  think  upon  such  themes  of 
his  own  accord.  In  hke  manner,  it  is  not  in  the  true 
course  of  nature  to  set  a  child  to  declaim  before  he 
has  any  ambition  or  desire  to  speak  for  himself,  his 
own  thoughts. 

The  most  instructive  reading,  for  a  person  of  any 
age,  old  or  young,  is  that  in  which  the  author's  tone 
of  thought  is  above  the  average  tone  of  the  reader's 
thought,  and  yet  not  beyond  his  grasp.  The  best  exer- 
cise for  a  child  is  to  commit  to  memory,  to  repeat,  but 
not  to  declaim,  such  selections,  of  poetry  or  prose,  as, 
although  not  altogether  above  his  comprehension,  are 
worth  being  treasured  forever  in  remembrance.  As 
a  general  rule  the  child  should  be  even  discouraged 
from  committing  to  memory  anything  except  passages 
from  the  Scriptures,  and  passages  of  sterling  poetry. 
The  Scriptures  he  may  commit  to  memory  ;  not  only 
for  their  intrinsic  value,  but  because  they  are  often 
appealed  to  as  authority,  and  when  so  used  should  be 
quoted  with  verbal  accuracy.  Good  poetry  may  be 
also  committed  to  memory,  because  a  part  of  its  value 
lies  in  its  felicitous  choice  of  expressions,  and  in  the 
melody  of  its  rhythm  ;  and  these  are  lost  unless  it  is 
quoted,  or  recalled  to  memory,  in  the  poet's  own 
language.  But  the  committing  to  memory  of  the 
words  of  ordinary  text-books,  or  of  inferior  poetry,  or 
of  school  dialogues  for  exhibition,  should  be  indulged 
only  at  the  rarest  intervals  ;  and  the  tc-acher  who  re- 
quires it  frequently  does  a  harm  to  the  pupil  far 
greater  than  he  imagines. 


LANGUAGE.  11/ 

The  best  exercise  in  composition  is  to  read  good 
authors  ;  that  is  the  only  real  '•  Aid  to  Composition." 
All  art  is  imitative,  and  the  great  essential  in  teach- 
ing it  is  to  set  good  models  before  the  pupil.  When 
the  pupil  has  read  something  which  is  worth  reading, 
let  him  close  the  book,  and  tell  what  he  has  been 
reading  about.  When  he  is  old  enough  to  write 
legibly,  let  him  write  upon  his  slate  some  brief  anec- 
dote from  memory,  after  reading  it.  Let  him  with  a 
ballad  before  him,  tell  the  tale  in  good  prose  ; — let 
him  write  in  prose  the  ideas  of  a  piece  of  poetry  lying 
before  him.  The  student  who  is  old  enough  to  write 
upon  a  given  theme,  will  find  after  reading  or  reflect- 
ing upon  his  subject,  no  preparation  for  writing  upon 
it,  so  effective  as  reading,  for  an  hour  immediately  be- 
fore taking  up  his  pen,  some  particularly  well  written 
essays  upon  similar  themes.  It  is  in  this  way  that  an 
inferior  poet  can  write  sometimes  an  admirable 
parody,  or  imitation,  of  a  superior  one ;  by  reading 
Shakspere,  or  Milton,  or  Tennyson,  for  an  hour  or 
two,  he  is  able  to  write  a  poem  of  his  own  in  the  style 
of  the  selected  author.  Indeed,  it  is  thus  that  all 
oratory  and  poetry,  even  among  the  princes  of  litera- 
ture, has  grown  ;  each  building  upon,  and  stimulated 
by,  the  labor  of  his  predecessors.  And  it  is  for  this 
reason,  as  well  as  others,  that  it  is  so  important  that 
the  child  should  have  before  him  in  the  books  which 
he  reads  at  home,  and  in  schools,  the  best  models  of 
pure  English  and  of  elevating  thought  ;  to  give  him 
the  ability  to  express  himself  gracefully,  that  is  to  say, 
with  ease  and  strenerth. 


Il8  TRUE  ORDER  OF  STUDIES. 

The  French  and  German  languages,  and  also 
Latin  and  Greek  are  taught  in  many  schools  in  this 
country.  Of  late  years  there  has  been  some  return 
to  rational  methods  in  teaching  languages  ;  and  yet  the 
mania  for  educational  drill  prevails,  even  now,  to  such 
an  extent,  that  I  may  be  pardoned  for  speaking  freely 
upon  it.  Twenty  years  ago  the  fashionable  mode  of 
learning  a  language  was  to  begin  by  committing  some 
text  book  upon  its  grammar  to  memory.  In  the 
case  of  Latin  this  grammar  involved  the  grammar 
of  the  whole  literature  from  the  oldest  writers, 
to  the  most  recent ;  in  Greek  it  involved  all  the 
various  dialects  of  the  different  countries,  as  well 
as  the  changes  in  the  more  recent  forms,  from  the 
more  ancient.  After  this  feat  of  memory,  the  pupil 
began  to  study  very  critically  some  author,  pausing 
over  each  sentence  and  word  to  apply  his  grammar  to 
the  explanation  of  the  construction.  Finally,  if  his 
life  and  his  patience,  were  long  enough,  he  began  to 
read  the  literature  of  the  language. 

The  more  natural  method  is  more  agreeable,  and 
more  rapid  in  producing  results.  The  pupil  begins 
by  reading  the  literature,  then  analysing  the  lan- 
guage, and  studying  its  grammar.  The  pronuncia- 
tion is  first  to  be  determined  ;  if  Greek  or  Latin,  some 
fixed  principles  must  be  adopted  ;  if  a  modern  lan- 
guage, we  should  get  as  nearly  as  possible  the  actual 
present  usage  of  the  best  speakers.  This  is  to  be 
gained  by  the  ear,  listening  to  native  speakers  ;  al- 
though great  aid  may  be  had  I  hope  in  the  not 
distant    future    from    Bell's   Visible  Speech.     While 


LANGUAGE.  I  I9 

learning  to  pronounce,  you  also  are  to  learn  to  trans- 
late ;  and  the  first  essay  is  to  be  upon  a  sentence,  not 
merely  upon  a  word.  Professor  Sauveur's  method  in 
teaching  French  conversation  is  a  perfect  method  of 
nature.  But  if  you  have  not  the  living  teacher,  and 
are  obliged  to  use  books,  begin  at  once  with  classic 
authors  and  translate  them,  without  grammar  or 
dictionary.  The  object  at  first  is  to  learn  the  lan- 
guage ;  to  get  if  you  can  the  meaning  of  the  particu- 
lar page  before  you,  not  for  its  own  sake,  but  for  the 
sake  of  learning  the  meaning  of  the  words.  Now, 
the  meaning  of  the  frequently  occurring  words  will 
be  fixed  in  the  memory  more  surely  by  repetition  of 
them,  in  reading,  than  by  looking  them  out  in  the 
dictionary.  Skip,  therefore,  the  words  and  sentences 
whose  meaning  is  not  clear  to  you  after  a  moment's 
thought ;  read  the  chapter  through  a  second  time,  and 
it  may  come  to  you.  Your  clew  to  the  meaning  is  to 
be  found  in  the  similarity  of  the  words  to  the  cognate 
words  in  the  vernacular  ;  and  this  method,  therefore, 
can  be  wholly  adopted  only  in  the  case  of  the  modern 
tongues  of  Western  Europe.  If  the  reader  of  this 
chapter  has  never  tried  it,  he  will  be  astonished  to 
find  how  readily  an  intelligent  American  boy,  know- 
ing only  English,  will  pick  out  a  part  of  the  meaning 
of  a  page  in  French,  German,  Danish,  Swedish, 
Italian,  Spanish  or  Portuguese,  and  how  rapidly,  if  he 
continues  the  trial  always  on  the  same  language,  half- 
an-hour  every  day,  the  proportion  of  the  page  which 
is  intelligible  to  him  will  increase. 

When  the  pupil  can  thus  read  the  language,  and 


I20  TRUE    ORDER    OF    STUDIES. 

understand  nearly  the  whole  of  what  he  reads,  he 
may  beghi  to  look  out  in  the  dictionary  the  meaning 
of  the  few  words  which  he  does  not  know  ;  and  then, 
also,  he  must  begin  to  study  the  grammar ;  after 
which  as  a  final  thing  he  may  begin  to  translate 
from  the  vernacular  into  the  foreign  tongue,  and  to 
write  in  it  original  compositions.  But  this  should 
not  be  done  until  the  scholar  can  easily  read  and 
understand  the  new  language  without  a  conscious 
translation  of  it  into  the  vernacular.  This,  however, 
is  to  be  obtained  by  keeping  up,  even  after  beginning 
to  study  critically  with  grammar  and  dictionary,  the 
habit  of  daily  taking  up,  also,  books  which  you  are  not 
studying,  and  reading  them. 

There  are  two  entirely  distinct  objects  to  be  kept 
in  view  while  studying  a  foreign  tongue  ;  the  acquisi- 
tion of  a  new  language,  and  increased  mastery  over 
your  own.  For  the  first  end,  you  need  to  pay  close 
attention  to  the  minutest  details  of  the  construction 
and  order  of  the  words  of  the  author  whom  you  are 
reading  ;  for  the  second,  to  express  his  thoughts  (oc- 
casionally, at  least,  and  in  his  finest  passages),  in  the 
best  and  most  idiomatic  English.  When  reading 
Plato,  Cicero,  Goethe,  or  Moliere,  you  wish  to  seize 
their  thoughts  precisely  as  they  uttered  them,  with 
the  words  in  their  very  order,  and  with  a  perception 
of  the  ideas  direct  from  their  words,  without  even  a 
mental  translation  into  your  own  tongue.  This 
power  is  acquired  by  the  combination  of  the  critical 
study  of  some  one  or  two  select  works  with  a  rapid, 
extensive  reading  of  the  other  writings  of  your  author. 


LANGUAGE.  121 

In  this  reading  for  the  sake  of  learning  the  new 
language,  the  translation,  if  one  occurs  to  your  mind, 
will  be  slavishly  literal,  and  if  you  should  utter  it  would 
be  less  intelligible  than  the  original  ;  like  Thomas 
Taylor's  translation  of  the  Divine  Dialogues,  in  which 
he  follows  the  author  so  literally,  that  the  English  is 
harder,  for  an  Englishman,  than  the  Greek.  But  if 
you  would  bave  the  study  aid  you  in  expressing  your 
own  thoughts,  you  must  also  at  times  accustom  your- 
self to  translate,  from  the  original,  the  thoughts  alone  ; 
putting  them,  with  fidelity  to  the  thought,  into 
English  entirely  remote  from  the  forms  of  your 
author,  and  peculiar  to  our  own  best  writers. 

These  directions  are  not  inapplicable  to  schools. 
In  the  Waltham  High  School  we  had  for  several  years 
a  teacher  whose  classes  would  bear  the  most  vigorous 
examination  in  all  the  niceties  of  philological  and 
grammatical  analysis,  and  would  also  read,  from  a 
Latin  or  French  author,  so  fluently  and  in  such  easy 
and  idiomatic  English,  that,  as  a  member  of  the  ex- 
amining committee,  I  not  unfrequently  felt  obliged  to 
inform  visitors  that  the  class  were  not  reading  from  a 
written  or  printed  translation.  The  teacher  should 
require,  in  a  spoken  or  written  translation,  one  thing 
or  the  other,  either  extreme  literal  accuracy,  or  else 
good  idiomatic  English.  Next  to  the  ability  to  act 
well,  must  be  placed  the  ability  to  speak  well  ;  indeed, 
so  interwoven  are  the  functions  of  the  human  being, 
that  the  ability  to  express  thought  increases  the 
ability  to  think  ;  and  the  power  to  think  increases  the 

power  to  act. 

6 


122  TRUE  ORDER  OF  STUDIES. 

That  which  pertains  most  strictly  to  the  general 
purpose  of  the  littl(j  volume,  however,  is  to  lay 
emphasis  upon  the  fact  that  in  the  order  of  nature  a 
child  hears  music  and  spoken  language  long  before  it 
has  the  power  to  study  and  analyse  them.  Whatever 
language  we  are  considering,  it  is  better  for  the  child 
to  be  taught  to  read  and  understand  it  in  its  larger 
scope  and  meaning  before  he  begins  to  give  it  a  criti- 
cal and  thorough  study.  He  must  learn  to  sing  and 
play,  before  he  is  ready  for  thorough  bass  and  counter- 
point. He  must  read  and  write  English,  before  he  is 
ready  for  grammar  and  rhetoric.  He  must  in  like 
manner  be  able  at  least  to  read  easily  any  other 
tongue  before  he  takes  up  its  grammar.  And  in  learn- 
ing to  speak  and  write  it,  he  must  confine  himself  to 
the  best  models  of  native  writers  and  speakers  until 
he  is  perfectly  familiar  with  them  ;  before  he  begins 
himself  to  use  it  in  expressing  his  thoughts. 


LAW.  153 


CHAPTER    XVI. 

LAW. 

THE  word  law  as  used  in  the  title  of  this  Chapter 
has  a  wide  significance,  including  the  whole 
history  of  the  state  ;  of  both  the  military  and  civil 
powers;  the  mode  in  which  human  society  has  been 
governed,  or  endeavored  to  govern  itself  in  all  ages. 

The  child  is  born  subject  to  his  parents  ;  and  the 
parental  government  has  always  been  a  type  ;  perhaps 
suggesting  and  leading  to  the  government  of  tribes 
and  nations.  At  all  events,  there  are  no  savages  to  be 
found  without  some  traces  of  government ;  and  in  all 
civilized  countries,  there  has  been  developed  the  idea 
of  impersonal  law ;  through  the  organization  of  a 
community  whose  associated  wisdom  shall  decide 
upon  what  is  right,  and  what  is  for  the  best  interests  of 
the  whole  ;  whose  associated  power  shall  enforce  the 
right,  and  develop  the  good,  so  far  as  the  limits  of  its 
ability  extend.  The  historical  study  of  these  relations 
of  men  to  each  other  is  necessary,  not  only  to  the  full 
development  of  the  student's  mental  powers  ;  but  as 
a  preparation  by  which  he  is  fitted  for  an  intelligent 
participation  in  the  rights  and  duties  of  those  relations; 
which  is  by  definition  the  chief  end  of  a  liberal  edu- 
cation. 


124  TRUE    ORDEK.    OF    STUDIES. 

The  method  of  nature,  in  this  branch  of  discipline, 
is  sufficiently  obvious.  The  child  is  born  into  a 
family, and  is  subject  to  his  parents;  they  require  of 
him  obedience  before  he  can  understand  the  ground 
on  which  the  authority  rests.  No  disciplinarian  of  the 
modern  school  has  as  yet,  I  believe,  published  a  text 
book  for  infants,  explaining  and  proving  to  them, 
while  yet  in  the  nurse's  arms,  the  logical  foundations 
on  which  they  are  required  to  submit  to  and  obey 
their  parents.  Here  is  one  retreat,  where  nature  and 
common  sense  retain  some  hold.  In  a  well  ordered 
family  the  child  learns  by  subjection  to  his  parents, 
the  duty  of  subjection  to  just  authority^  and  forms  a 
habit  of  obedie.ice.  He  is  brought  under  the  order 
and  discipline  of  the  family,  before  he  can  rise  to  the 
perception  of  that  vast  scheme  of  universal  order, 
planned  by  Infinite  wisdom,  in  obedience  to  an  im- 
pulse of  unfathomable  love,  and  carried  into  execution 
by  Almighty  Power ; — that  Universal  Order,  after 
which  all  wise  legislation  strives  ;  according  to  which 
all  just  judicial  decisions  are  framed  ;  and  which  all 
righteous  executive  power  seeks  to  embody. 

Thus  also  in  the  school.  The  first  and  most  im- 
portant ideas  of  law,  gained  there,  come  not  from 
histories  and  constitutions,  political  essays  or  orations; 
but  from  the  wise  and  just  discipline  of  the  school 
room  ;  from  the  rules  of  play  observed  in  the  games 
of  the  school  children  ;  and  from  the  perception  that 
the  parents  and  teachers  are  also  the  subject,  even  in 
school  matters,  to  the  regulations  of  the  committee, 
the  votes  of  the  town,  and   the  laws  of  the  common- 


LAW.  125 

wealth.  The  judicious  teacher,  by  occasional  words, 
rightly  directing  the  child's  attention,  for  a  moment, 
to  such  themes,  giving  an  incidental  instruction  in 
politics  and  law,  does  an  important  work  for  the  State, 
and  for  her  children. 

Under  this  department  comes  also  History  in  the 
ordinary  sense  of  the  word.  The  "  History  of  the 
World "  is  too  vast  a  field  for  survey  as  a  mere 
part  of  liberal  education.  In  selecting  nations  and 
periods  which  shall  be  most  useful  to  the  general 
student,  it  is  manifest  that  we  should  confine  ourselves, 
principally,  to  the  direct  line  of  spiritual  inheritance, 
the  sources  whence  we  derived  our  science  and  laws. 
The  United  States,  particularly  in  the  periods  when 
the  Colonies  were  taking  consolidated  form,  and  when 
they  were  achieving  their  independence,  and  becom- 
ing a  nation  :  Great  Britain,  especially  in  the  sixteenth 
and  seventeenth  centuries  ;  Rome  in  the  age  of  Caesar 
and  Augustus  ;  Greece  just  before,  and  during  the 
age  of  Pericles  ;  and  Israel  from  the  days  of  Moses  to 
those  of  Solomon  ;  these  are  topics  on  which  every 
man,  who  takes  any  interest  in  the  welfare  of  our  dear 
land,  ought  to  be  early  well  informed.  They  all  bear 
directly  upon  the  questions  of  to-day  in  a  Republican 
Government.  Before  the  young  man  leaves  the  High 
School  he  should  also  take  a  brief  course  of  study  in 
constitutional  law  ;  comparing  the  constitutions  of  our 
States,  and  of  the  United  States,  with  those  of  Great 
Britain,  Rome,  Greece,  and  the  early  Hebrew  Com^ 
monwealth.  The  simplicity  of  our  constitution  brings 
this  study  within  the  reach  of  all  minds  ;  and  the  im- 


126  TRUE  ORDER  OF  STUDIES. 

portance  to  the  nation  of  having  the  knowledge  of  the 
constitution  diffused  among  the  people  makes  it  an 
imperative  duty  for  every  High  School  graduate  to 
have  read  carefully  some  simple  and  sound  commen- 
tary upon  it. 


POLITICAL   ECONOMY.  12/ 


CHAPTER  XVII. 

POLITICAL     ECONOMY. 

BESIDES  the  government  of  man  by  man,  the 
older  pupil  will  see  that  men's  affairs  are  also 
governed  by  laws  not  altogether  under  their  control. 
He  will  find  at  one  time  the  community  apparently 
prosperous,  and  after  a  year  or  two  will  hear 
that  business  is  dull.  He  will  hear  allusions 
made  to  the  time  when  gold  and  silver  coin  were 
used  freely,  as  the  fractional  paper  currency  is  to-day. 
At  the  time  when  elections  for  Congress  are  about 
to  take  place  he  will  hear  earnest  debates  concerning 
the  currency,  or  concerning  protection  and  fi;ee  trade. 
It  is  not  well  that  the  young  man  in  the  public 
school  should  have  angry  political  passions  aroused  ;  or 
become  a  partisan  upon  either  side,  blinded  to  all  con- 
sideration of  truth  as  held  by  his  opponents.  But 
there  are  fundamental  truths,  established  by  the  clear 
thought  of  Adam  Smith,  and  Henry  C.  Carey  (the 
two  most  solid  thinkers  upon  these  subjects),  which 
are  valuable  to  every  citizen  ;  and  no  sound  decision 
concerning  such  debatable  questions  can,  except  ac- 
cidentally, be  reached  by  one  who  does  not  learn  these 
truths.  Some  of  these  vital  propositions  are  jDerfectly 
within  the  comprehension  of  children,  and  ought  to  be 


128  TRUE  ORDER  OF  STUDIES. 

taught  in  the  public  schools,  as  a  protection  against 
multiform  errors  introduced  by  English  writers,  and 
popularized  in  tales  and  newspapers  of  the  present 
day. 

The  government  of  man  by  men  is,  of  course,  liable 
to  error ;  mistaken  legislation  and  arbitrary  acts  of 
military  and  executive  power,  may  therefore  occasion- 
ally interfere  with  the  operation  of  the  natural  and 
wholesome  laws  of  commerce.  Persons  living  in 
countries  in  which  the  course  of  legislation,  and  of 
custom,  has  long  been  in  an  erroneous  direction,  will 
be  likely  to  mistake,  and  misunderstand,  the  natural 
laws  ;  and  this,  as  we  Americans  think,  is  the  condi- 
tion of  persons  living  in  Great  Britain,  where  laws  of 
primogeniture,  entailment  of  estates,  difficulties  in 
conveyancing,  guilds  and  trades  unions,  so  utterly 
prevent  freedom  of  trade  in  the  two  prime  raw 
materials,  land  and  labor,  as  absolutely  to  prevent  an 
Englishman  from  knowing  what  freedom  means.  We 
draw  from  our  fatherland  a  rich  inheritance  of  political 
and  civil  freedom  ;  but  we  also  draw,  at  the  present 
day,  many  false  opinions  in  specious  dress.  The 
firmness  with  which  an  Englishman  adheres  to  a 
theory,  or  to  a  custom,  or  to  a  supposed  right,  is  an 
excellent  element  in  his  character,  making  the  pro- 
gress of  the  nation  stable  ;  but  it  is  an  inconvenient 
element,  when  he  gets  started  in  a  wrong  direction. 

The  youngest  child  may  be  taught  how  to  place  a 
just  estimate  upon  the  worth  of  things  ;  that  a  thing 
is  useful  in  proportion  as  it  gratifies,  or  enables  you  to 
gratify,   healthy   human   desires  ;    and  thus  promote 


POLITICAL    ECONOMY,  I29 

human  happiness.  Thus  an  article  which  can  be  used 
for  an  indefinite  time,  and  by  a  multitude  of  persons, 
(for  example,  a  book,  a  picture,  a  statue),  is  worth  in- 
comparably more  than  a  thing  which  is  used  but  once, 
and  that  only  by  a  single  person  ;  even  if  the  price  in 
money  be  the  same.  The  usefulness  of  a  thing  is  its 
ability  to  serve  human  needs,  and  may  exist  in  the 
highest  degree  in  things  like  air  and  sunshine  that  are 
generally  without  price.  Price  is  the  measure,  in  gold 
or  silver,  of  the  commercial  value.  Value  is  the 
measure  of  the  difficulty  of  reproducing  a  useful 
thing.  Wealth  consists  in  the  ability  to  command  the 
services  of  natural  agents.  The  whole  life  of  a  civilized 
community  depends  upon  commerce  ;  upon  the  inter- 
change of  men's  services,  by  which  each  does  some- 
thing that  others  desire  him  to  do,  and  receives  from 
them  in  return  what  he  desires.  The  instrument  by 
which  this  is  accomplished  is  coin.  The  persons 
through  whom  the  commerce  is  effected  are  trades- 
men, or  merchants,  and  common  carriers.  The  fewer 
of  these,  and  the  nearer  that  producers  and  consumers 
are  brought  together,  the  more  advantageous  is  the 
commerce.  No  country  on  earth  is,  or  probably  ever 
will  be,  over  populated  ;  and  the  poverty,  vice,  and 
crime  of  nations  ;  their  decay ;  and  the  depopulation 
of  countries,  arises  from  misgovernment,  tyranny 
legislation  to  encourage  foreign  trade  ;  and  other 
errors  of  men.  Such  truths  as  these,  and  others 
equally  valuable,  may  be  incidentally  presented,  and 
illustrated  by  occurrences  in  the  course  of  the  school 
life,  or  by  passages  in  the  school   histories  ;  and  wil! 

6* 


130  TRUE  ORDER  OF  STUDIES. 

enlarge  the  minds  of  the  young  men,  and  prevent  their 
being  afterwards  ensnared  by  the  sophisms  of  those 
who  still  re-echo  Ricardo  and  Malthus,  or  still  hold 
that  foreign  trade  is  more  important  than  internal 
commerce. 


PSYCHOLOGY.  13I 


CHAPTER  XVIII. 

PSYCHOLOGY. 

A  CHILD  of  six  years  old  recently  asked  "  How 
do  you  know  that  any  thing  is  there,  where 
you  see  it  ? "  The  question  seemed  to  indicate 
precocious  metaphysical  development;  and  there  can  be 
no  question  that  a  precocious  metaphysical  spirit  of 
psychological  introversion,  is  as  much  to  be  deprecated, 
as  the  premature  study  of  physiology.  But  the 
anecdote  shows  that  such  questions  arise  at  a  very 
early  age,  and  the  judicious  teacher  may  find  some 
better  way  of  quieting  the  doubts  and  conflicts  than 
by  absolute  silence,  or  by  laughing.  Children  suffer 
very  much  from  dreams,  and  from  waking  visions  in 
the  dark  ;  especially  if  they  have  been  unfortunate 
enough  to  hear  or  read  stories  of  elves,  witches, 
ghosts,  dragons,  and  the  like.  They  are  afraid  to 
speak  of  the  matter,  and  endure  the  agony  in  silence. 
Many  an  otherwise  sunny  childhood  has  been  clouded 
by  these  visions  ;  the  child  being  haunted  at  night  by 
a  fear  that  the  vision  was,  after  all,  a  finer  reality  ;  or, 
like  the  boy  whom  I  have  mentioned,  that  the 
realities  of  the  day  were  as  unsubstantial  as  the 
visions  of  the  night.  "  Mother,"  said  another  child, 
on  awaking,  "  I   thought   that  this  world  was  God's 


132  TRUE    ORDER    OF    STUDIES. 

dream."  I  could  give  many  anecdotes  to  a  like  im- 
port. And  some  children  still  retain  the  faith  which 
men  formerly  held,  that  dreams  are  visitations  by 
night,  of  spiritual  beings.  Even  at  the  present  day 
there  are  men  who  hold  that  view. 

It  has  seemed  to  me  that,  in  consideration  of  the 
great  suffering  of  childhood  from  that  which  Hamlet 
so  much  dreaded,  bad  dreams,  we  might,  quite  early, 
give  the  child  enough  of  psychology  to  explain  to  him 
the  harmlessness  of  these  monsters.  He  knows,  be- 
fore he  goes  to  school,  that  there  are  brains  in  his 
skull.  He  might  upon  some  incidental  opportunity 
be  told  that  when  he  is  thinking,  he  is  moving  his 
brain,  as  truly  as  that  when  walking  he  is  moving  his 
legs.  And  that  as  sitting  still  is  resting  the  legs,  so 
stopping  all  thinking,  which  is  sleeping,  is  resting  the 
brain.  Then  he  may  have  observed  in  himself,  or  in 
a  very  tired  dog,  on  dropping  asleep,  a  twitching  of 
the  legs  ;  so  in  a  very  tired  brain,  there  is  a  twitching, 
a  motion  ;  and  that  partially  arouses  it,  and  sets  it  to 
half  conscious  imaginations,  which  are  dreams  or 
visions  ;  they  are  his  own  fancies  and  imaginations 
when  he  is  so  nearly  asleep,  that  he  does  not  know  they 
are  his  ;  but  they  cannot  really  hurt  him,  any  more 
than  his  playful  make  believes  when  awake. 

This  explanation  will  still  leave  certain  points  con- 
cerning dreams  as  great  a  mystery  as  ever  ;  they  may 
be,  as  Emerson  has  pronounced  them,  an  inexplicable 
one  ;  but  this  partial  explanation,  not  carrying  the 
child  into  much  introversion,  may  yet  enable  him  to 
bear  with  more  composure  this  annoying  symptom  of 


PSYCHOLOGY.  1 33 

fatigue,  of  over  excitement,  of  too  heavy  a  supper,  or, 
still  more  frequently,  of  a  slight  cold  disturbing  the 
digestion. 

Truly  metaphysical  inquiries  belong  to  so  late  a 
period  of  the  course  of  education  that  I  do  not  care  to 
speak  of  them  in  this  book,  which  is  principally  taken 
up  with  the  studies  of  the  younger  pupils. 


134  TRUE  ORDER  OF  STUDIES. 


CHAPTER  XIX. 

AESTHETICS. 

THE  perception  of  beauty  shows  itself  at  an  early 
age.  I  have  known  a  child  whose  first  articu- 
late word  was  the  exclamation  "  pretty  !  "  on  seeing  a 
bright  nosegay.  The  analysis  of  beauty,  as  the  em- 
bodiment of  a  simple  law  in  a  variety  of  details,  is  the 
work  of  a  mature  mind.  Erasmus  Darwin  attributes 
the  sense  of  beauty  to  the  association  of  the  ideas  of 
the  pleasures  of  satiety  in  the  infant,  with  the  curved 
outlines  and  soft  contour  of  the  mother's  breast. 

This  theory  would  deprive  the  infant  brought  up 
by  hand,  of  all  appreciation  of  beauty  ;  therefore  the 
modern  followers  of  that  eccentric  philosopher, 
supply  an  inheritance  of  instinctive  ideas  derived 
from  grandparents  who  were  more  fortunate  in  their 
infancy.  This  discussion  of  the  nature  of  the  sense 
of  beauty  is  not  required  for  education  ;  but  the 
culture  of  that  sense  is  requisite  ;  and  if  the  child's 
taste  is  properly  cultivated,  and  he  have  native  deli- 
cacy of  perceptions,  and  depth  of  feeling,  he  will  when 
old  enough  to  think  for  himself  give  a  very  different 
account  of  the  origin  and  nature  of  the  perception  of 
beauty.  He  will  discover  then  that  the  sense  of 
beauty  is  awakened  only  by  those  objects  which  show 


AESTHETICS.  135 

a  thought,  simple  in  itself,  embodied  in  variety  of  de- 
tail ;  so  that  it  is  an  intellectual  pleasure  in  the 
presence  of  a  work  of  intellect- 

To  cultivate  the  taste  for  beauty,  care  should  be 
taken  in  the  furnishing  of  the  school  house,  the  hang- 
ing of  its  walls ;  and  if  it  be  a  country  school-house, 
in  the  arrangement  of  its  grounds.  Of  two  text  books, 
in  other  respects  equal,  that  is  to  be  preferred  which 
has  a  well  proportioned  page,  and  that  in  which  the 
illustrations  are  well  drawn.  In  the  selection  of  copies, 
whether  drawn  or  natural  objects,  choose  those  which 
are  of  normal  and  beautiful  forms.  If  you  have 
chromos,  or  paintings,  on  your  walls,  let  them  be  not 
only  beautiful  scenes,  but  well  and  harmoniously 
colored. 

Frobel's  gifts  are  arranged  with  reference  to  color 
as  well  as  form.  I  have  for  twenty-five  years  past 
been  accustomed  to  try  direct  experiments  on  the 
beauty  of  form  and  color  as  perceived  by  scholars. 
For  example  I  place  a  long  rectangle  in  sight,  (say  of 
stiff  paper  tacked  on  the  blackboard)  and  covering  one 
end,  (say  by  a  slate  without  a  frame)  I  shorten  the 
rectangle,  and  ask  the  pupil  to  decide  at  what  length 
it  is  of  best  proportions.  In  the  judgment  of  seven 
out  of  ten,  the  best  proportion  is  that  in  which  the 
diagonal  divides  the  right  angle  in  the  ratio  of  very 
small  integral  numbers.  To  give  another  example,  I 
have  taken  two  circles  of  card  of  equal  size,  and  drawn 
in  each  a  central  circle  of  just  half  the  area.  In  one 
I  paint  the  central  circle  purple,  the  outer  ring  yellow  ; 
in  the  other,  the  centre  yellow,  the  outer  part  purple  ; 


136  TRUE  ORDER  OF  STUDIES. 

being  careful  to  use  precisely  the  same  shades  on  each 
card.  I  ask  the  pupil  to  compare  the  effect  on  his 
feelings  produced  by  looking  at  the  one,  and  at  the 
other.  Nearly  every  child  will,  without  knowing  what 
others  have  said  before  him,  say  that  the  one  is  con- 
strained, sad,  depressing,  autumnal ;  the  other  free, 
cheery,  summer-like. 

A  series  of  experiments  of  this  kind  awakens  in 
the  pupils  a  new  interest  in  the  beauty  of  nature  and 
of  art,  and  rapidly  cultivates  and  improves  the  taste. 
Of  course  this  is  merely  rudimental,  and  not  to  be 
considered  as  taking  the  place  of  the  higher  art  cul- 
ture which  should  follow  in  those  who  have  the  taste 
and  the  means.  At  every  step  in  the  course  of  draw- 
ing lessons,  a  judicious  teacher  may  by  skilful  ques- 
tions or  suggestions  lead  the  pupil  to  a  keener  appre- 
ciation of  the  beauty  of  form.  But  let  the  criticism  be 
always  guided  to  the  perception  of  beauties,  not  to  the 
exaggeration  of  defects. 

The  lessons  in  singing  give  also  constant  oppor- 
tunities for  aesthetic  reading.  First  in  regard  to  mere 
purity  and  smoothness  of  tone  ;  it  should  be  remem- 
bered that  there  is  a  beauty  in  the  mere  quality  of 
a  monotone,  just  as  there  is  beauty  in  mere  purity  of 
color  ;  and  this  is  not  a  matter  of  whim  or  association 
of  ideas  ;  but,  both  in  sound  and  color,  arises  from 
what  may  be  called  an  unconscious  perception  of  the 
rhythmical  character  of  the  motion.  The  greatest 
pains  should  be  taken  to  check  all  loudness,  harsh- 
ness, roughness :  natural  smoothness  in  the  early  at- 
tempt   to   sing    being   much    more   important    than 


AESTHETICS.  137 

correctness  of  integrity  or  of  harmony  Secondly, 
pains  should  be  taken  to  have  the  melodies  and  the 
words  adapted  to  each  other,  and  that  both  are  good. 
The  Music  Readers  for  the  Boston  Schools  are  com- 
mendable in  this  respect,  as  are  also  many  of  the  older 
collections  of  Church  music.  But  there  is  also  a  style 
of  music  and  of  hymns  popular  in  the  churches  and 
Sunday  Schools  to-day,  to  which  I  have  already 
alluded,  as  having  a  debasing,  demoralizing  effect. 
The  words  are  vapid,  or  strained,  not  in  idiomatic 
English  ;  and  the  music  is  of  the  same  character,  a 
mere  haphazard  writing  of  the  notes,  and  subsequent 
division  into  measures.  We  have  in  these  instances 
neither  English  melody  nor  German  harmony  ;  but  a 
composition  which  has  been  well  described  as  having 
the  flavor  of  boiled  water.* 

I  have  found  it  advantageous  to  ask  pupils  to  give 
their  opinion  on  the  meaning  of  a  melody,  new  to 
them,  and  of  which  they  knew  nothing,  except  as  they 
heard  it  for  the  first  time  upon  a  piano;  and  I  have 

*  Lest  I  seem  to  strike  in  the  dark,  let  me  quote,  first  an  en- 
tire chorus  from  a  popular  hymn  to  the  Saviour : — "  Ever  near 
us,  guide  and  cheer  us,  Touch  our  eyes  that  we  can  see;  If 
thou  charm  us,  naught  can  harm  us.  Still  the  Father  calls 
through  thee."  The  meaning  of  the  word  "charm"  in  this 
chorus,  and  the  connection  of  the  fourth  line  with  the  other 
three,  passes  my  comprehension  ;  as  does  the  following  popular 
illustration  of  the  aphorism  that  "  Bright  things  can  never  die  "  : 
•'  Many  a  happy  thing.  Many  a  daisy  spring,  Float  o'er  time's 
ceaseless  wing.  Far,  far  away."  May  such  poetry  keep  far  away 
from  me  and  mine.  What  a  contrast  between  these  two  stanzas 
and  the  songs  of  Watts,  or  Mrs.  Follen. 


138  TRUE    ORDER    OF    STUDIES. 

heard  of  a  good  teacher,  who  always  required  her 
pupils  thus  to  judge  of  a  piece,  before  they  heard  its 
name,  or  attempted  to  play,  or  sing  it.  Every  melody 
has  an  expression  of  its  own,  heightened  and  modified, 
but  not  essentially  altered,  by  harmony,  and  by  orches- 
tration. The  melody  thus  answers  to  outline,  har- 
mony to  light  and  shade,  orchestration  to  coloring. 
Bring  into  the  school  frequently  the  portraits,  photo- 
graphed, engraved,  or  lithographed,  of  various  persons 
of  marked  character  known  to  you ;  and  let  the 
scholars  without  hint  or  clew,  tell  you  how  the  face 
impresses  them.  They  will  doubtless  surprise  you 
by  the  accuracy  with  which  they  will  often  describe 
the  real  character  of  the  person.  In  the  same  way, 
sing  or  play  to  them  music  of  good  character,  written 
by  composers  of  merit,  for  specific  words  or  specific 
occasions,  and  let  the  pupils,  without  hint  or  clew, 
tell  you  how  the  music  sounds  to  them, — what  feeling 
it  expresses,  or  for  what  occasion  it  seems  adapted. 
This  will  increase  very  much  their  appreciation  of 
music,  and  its  usefulness  to  them. 

I  have  spoken  of  the  use  of  classics  as  reading 
books ;  Mrs.  Barbauld  and  Miss  Edgeworth  for 
younger  scholars ;  Shakspeare  and  Wordsworth  for 
older  classes.  If  you  have  not  this  privilege,  but  must 
use  the  ordinary  collections,  let  the  class  read  two 
pieces  of  very  unequal  literary  merit,  and  then  call 
upon  them,  without  hint  of  your  own  opinion,  to  give 
their  judgment  as  to  the  respective  style  and  finish  of 
the  two  pieces.  After  they  have  given  their  opinion, 
give  them  the  benefit  of  yours. 


ETHICS.  139 


CHAPTER  XX. 

ETHICS. 

AS  we  approach  the  higher  branches  of  the  hier- 
archy we  come  as  I  remarked  concerning 
Political  Economy,  to  disputed  questions  ;  and  are  to 
be  careful  not  to  arouse  partisan  feelings,  nor  to  give 
doubtful  opinions  for  settled  truths.  There  are  various 
theories  as  to  the  logical  foundation  of  ethics,  but  the 
discussion  of  those  theories  is  to  come  only  in  an  ad- 
vanced stage. 

At  the  child's  entrance  into  school  he  has  learned 
the  meaning  of  the  words  "you  must,"  and  "you 
ought."  He  has  a  dim  sense  of  the  difference  be- 
tween a  mistake  and  a  sin,  between  want  of  taste  and 
want  of  principle.  The  teacher  who  begins  to  reason 
with  him  at  once,  and  explain  to  him  the  fundamental 
theories  of  ethics,  will  probably  do  him  harm,  and 
make  him  doubt  the  reality  of  ethical  distinctions. 
The  natural  mode  of  procedure  is  to  deepen,  first  of 
all,  as  far  as  you  are  able,  his  sense  of  obligation,  of 
duty.  Let  him  see  that  you  feel  it  binding  upon  you  ; 
and  that  nothing  earthly,  or  unearthly,  could  tempt 
you  to  do  what  you  are  clearly  convinced  is  wrong. 
Feelings  and  sentiments  are  contagious ;  the  char- 
acter of  the  teacher  is,  in  spite  of  himself,  reflected  in 


1 40  TRUE    OROER    OF    STUDIES, 

some  degree  in  the  character  of  his  pupils.  I  once 
asked  a  teacher,  who  succeeded,  incomparably  better 
than  any  other  teacher  I  ever  knew,  in  keeping  the 
clothes  and  faces  of  her  pupils  clean,  the  school-house 
and  outbuildings  perfectly  undefaced,  how  she  did  it. 
"  I  don't  know,  Mr.  Hill,"  was  her  honest  answer,  "  1 
do  7iot  try  to  do  it."  Then,  after  a  pause,  she  added, 
modestly,  "  there  is  perhaps  one  thing,  I  am  always 
scrupulously  neat  myself."  That  was  doubtless  the 
secret  ;  her  own  person,  her  dress,  her  desk,  and  table, 
her  books,  were  always  perfectly  clean  and  in  perfect 
order. 

Thus  also  the  teacher  who  has  himself  seen  the 
awful  sanctity  of  the  moral  law,  and  felt  that  in  spite 
of  all  which  utilitarians  and  sensationalists  may  say,  a 
man  had  better  die,  and  be  annihilated,  than  deliber- 
ately to  do  what  he  clearly  knows  to  be  wrong,  he 
will  without  lectures,  sermons,  or  twaddle,  impart  to 
his  pupils  the  same  sentiment.  If  you  would  know 
the  reality  and  cursedness  of  sin,  the  nobility  and 
glory  of  virtue,  said  my  Latin  tutor  to  me,  read  the 
"  Agricola,"  of  Tacitus.  You  can  see  it  in  the  lives  of 
men,  you  cannot  learn  it  from  their  lips. 

Mary  Wolstonecraft  carried  out  that  idea  in  her 
"  Elements  of  Morality  "  ;  which  was  a  series  of  por- 
traitures of  vices  and  of  virtues,  woven  into  a  story  of 
Mr.  Jones,  a  merchant  in  Bristol.  The  same  thing  was 
well  done  for  American  schools  by  M.  F.  Cowdrey, 
of  Sandusky,  Ohio ;  his  anecdotes  were  not,  however, 
interwoven  in  a  story.  The  fascination  of  the  modern 
novel  and  tale  is  in  the  portraiture  of  characters  which 


ETHICS  141 

they  present,  "  holding  the  mirror  up  to  nature  "  ;  and 
if  it  is  truthfully  done,  giving  the  hideous  aspects  of 
sin,  and  the  attractive  side  of  goodness,  it  is  a  good 
work.  A  novel  is  thus  a  potent  agency,  for  good,  or 
for  evil.  The  same  may  be  said,  in  its  degree,  of  the 
little  stories  which  are  told  in  a  child's  hearing,  or 
embodied  in  the  books  which  it  reads.  Good  morals 
and  good  manners  come  first  of  all  in  the  objects  to 
be  sought  in  the  public  schools,  but  they  are  most 
successfully  taught  by  the  teacher  taking  the  greatest 
pains  first  to  be  irreproachable  himself.  The  art  of 
living  well,  like  other  arts,  is  learned  by  iniitation  of  a 
good  model ;  and  a  living  object  is  the  best  model  in 
all  cases, — if  accessible. 


142  TRUE    ORDER    OF    STUDIES. 


CHAPTER  XXI. 

THEOLOGY, 

IT  is  difficult  to  separate  morality  from  religion  ; 
even  the  idolatrous,  and  semi-atheistic  Chinaman 
sanctions  his  moral  precepts  by  religious  doctrines  ; 
and  a  Chinaman  who  had  thrown  off  his  idolatry,  and 
for  a  time  rested  in  pure  atheism,  told  me  that  he  felt 
during  that  time  no  moral  restraint ;  and  that  his 
sense  of  duty  and  obligation  did  not  return,  until  two 
or  three  years  afterwards,  when  he  was  converted,  by 
the  simple  sublimity  of  the  first  chapter  of  Genesis, 
to  a  faith  in  Theism,  and  then  to  Christianity. 

Debates  have  arisen  in  America  within  a  few  years 
concerning  the  use  of  the  Bible  in  schools  ;  concern- 
ing the  introduction  of  the  idea  of  God  into  the  public 
teaching ;  concerning  the  separation  of  the  public 
school  funds  and  the  payment  of  a  part  of  the  income 
to  the  support  of  Church-schools.  The  second  of 
these  questions  alone  comes  within  the  direct  scope  of 
this  volume  ;  but  I  am  not  unwilling  to  record  my 
opinion  upon  the  other  two. 

It  seems  tome  that  public  education  is  a  necessity 
in  a  republican  government ;  that  the  expenses  there- 
of should  be  met  by  a  tax  levied  upon  all  ;  and  that 
the  proceeds  of  that  tax  should  be  expended  only  in 


THEOLOGY.  I43 

the  support  of  schools  entirely  within  the  control  and 
management  of  persons  elected  by  the  public  vote. 

It  seems  to  me  that  while  the  reading  of  the  Bible 
is  not  a  necessity  in  public  education,  it  is  highly  fit 
and  proper  that  a  portion  of  that  book  should  be  daily 
used  liturgically  in  the  public  schools  of  a  Christian 
community.  The  selections  from  the  Bible  by  Joseph 
T.  Buckingham  were  used  in  Waltham,  with  happy 
effect ;  the  selections  by  the  Rev.  D.  G.  Haskins 
seem  to  me  admirably  made  for  school  purposes.  Our 
rule  in  Waltham  was  that  no  child  should  be  com- 
pelled to  read,  if  his  parents  objected,  and  we  even 
allowed  those  children,whose  parents  wished  it,  to  enter 
school  after  the  morning  reading.  The  promulgation 
of  this  vote  put  an  immediate  stop  to  all  complaints  ; 
and  no  parents  ever  availed  themselves  of  the  privilege. 
"  Sat  erat  potuisse  videri."  If  my  memory  serves  me, 
the  same  thing  took  place  at  Antioch  College  ;  a  parent 
objected  to  his  son  being  obliged  to  attend  morning 
prayers.  "  If  I  had  wanted  him  to  study  theology." 
he  wrote,  "  I  could  have  done  it  cheaper  at  Oberlin." 
I  replied,  that  the  young  man  was  not  obliged  to 
attend  prayers,  if  either  he,  or  his  father  had  con- 
scientious scruples.  That  closed  the  matter  ;  and  the 
young  man  attended,  when  he  found  that  he  was  not 
under  constraint. 

But  in  regard  to  the  third  question,  the  exclusion 
of  Theistic  teaching,  the  case  is  different.  We  have 
among  us  conscientious  persons  who  demand  the 
entire  secularization  of  the  schools  ;  they  would  ex- 
•^lude  sectarianism  by  excluding  Religion.     I  cannot 


144  TRUE  ORDER  OF  STUDIES. 

but  regard  this  as  a  fundamentally  erroneous  position, 
founded  on  radically  defective  postulates. 

The  education  which  the  safety  of  the  republic 
demands,  for  every  one  of  its  children,  is  a  liberal 
education  ;  that  is,  an  education  becoming  a  freeman  ; 
an  education  fitting  one  for  the  duties  of  a  citizen. 
First  of  all,  in  the  requisites  of  such  an  education,  it 
must  impress  upon  the  future  citizen  the  inviolable 
sanctity  of  law,  the  reality  and  eternal  worth  of 
justice,  the  necessity  of  maintaining  the  rights  of 
others  as  well  as  your  own.  Now  in  my  opinion,  and 
in  the  opinion  of  a  vast  majority  of  intelligent  men, 
this  cannot  be  done,  unless  the  chUd  be  led  to  recog- 
nize reverently  the  being  of  God,  the  all  seeing  Wit- 
ness and  Judge,  as  the  first  and  greatest  of  all  truths  ; 
the  widest  and  most  firmly  established  of  all  indue 
tions  ;  the  clearest  and  most  certain  of  all  intuitions. 
Herbert  Spencer,  who  is  considered  by  most  of  his 
readers  as  an  anti-theistic  writer,  declares  the  being 
of  an  Ultimate  cause  of  the  universe,  to  be  avouched 
to  us  by  a  strength  of  evidence,  greater  than  that  for  any 
other  truth  ;  so  that  we  are  more  sure  of  the  existence 
of  such  a  cause,  than  we  are  of  our  own.  Moreover 
the  same  writer  declare^  that  there  is  no  vice  in  the 
constitution  of  things,  but  that  every  thing  moves 
forward  towards  better  ends  for  the  human  race 
Thus  the  leading  opponent,  in  England,  of  theistic 
views,  virtually  acknowledges  that  the  existence  of  a 
wise  and  beneficent  origin  and  cause  of  the  universe 
is  the  most  certain,  and  most  compiehensive  of  all 
truths.     It  is,  I  maintain,  the  simplest  wisdom  to  give 


THEOLOGY.  1 45 

to  this  grandest  and  most  certain  of  truths,  a  single 
word,  or  name  ;  that  is  to  teach  the  child  to  refer  all 
the  wondrous  harmonies  of  the  universe,  and  its  bene- 
ficent laws  of  operation  to  God  ;  to  teach  him  to  re- 
gard God  as  ever  present,  ever  a  witness  even  to  his 
thoughts,  and  ever  being  so  wise,  and  so  just,  and  so 
merciful,  that  he  will  make  it  turn  out  well  in  the  end 
for  those  who  adhere  to  the  law  of  right,  evil  for  those 
who  persist  in  doing  evil.  The  child  will,  of  course, 
attach  crude  and  false  conceptions  to  this  great  name. 
But  they  will  be  incomparably  less  crude,  and  less 
false,  than  those  which  he  will  form  for  himself,  if  un- 
taught. The  superstition  of  a  child  brought  up  re- 
ligiously may  be  lamentable,  but  that  of  a  child  brought 
up  atheistically  is  horrible. 

The  existence  of  sectarian  disputes  about  religion, 
and  of  partisan  contests  in  politics,  no  more  forbids 
the  introduction  of  religion,  political  economy,  and 
constitutional  law,  into  schools,  than  the  existence  of 
scientific  differences  of  opinion  forbids  the  introduc- 
tion of  science  into  schools. 

Some  believe  that  geometry  deals  with  space,  and 
the  rado  of  circumference  to  diameter  is  about  that 
of  22  to  7;  others  believe  that  geometry  deals  with 
dimensions,  and  that  the  ratio  is  that  of  3  to  i  ;  some 
think  it  best,  in  subtraction,  when  the  subtrahend 
figure  is  smaller,  to  add  ten  mentally,  first  to  the 
minuend,  then  to  the  subtrahend  ;  others  prefer  to 
transpose  mentally  one  of  the  tens  in  the  minuend. 
In  spite  of  these  differences  of  opinion,  geometry  and 
arithmetic  continue  to  be  the  foundation  of  all  human 

7 


146  TRUE    ORDER    OF    STUDIES. 

learning  and  necessarily  occupy  the  earliest  place  in 
our  course  of  education.  The  same  may  be  said 
(m.  m.)  of  every  branch  of  science.  And  above  all, 
unless  political  economy,  constitutional  law,  ethics,  and 
theology,  crown  the  education  of  the  young  man^ 
then  the  whole  course  of  his  culture,  so  far  as  regards 
the  interests  of  the  state  and  of  the  community,  which 
has  borne  the  cost  of  his  education,  is  concerned,  is 
worthless  ;  it  has  stopped  short  of  the  point  for  which 
all  the  course  is  established.  The  Westminster 
Assembly's  first  question,  and  answer,  agree  with  the 
saying  of  St.  Paul,  concerning  the  Creator,  that  of 
Him,  and  Him,  and  for  Him,  are  all  things  ;  not  a 
step  can  be  rightly  taken  but  in  explicit,  or  implicit, 
obedience  to  that  truth.  The  test  of  scientific  theories 
is  their  conformity  to  the  Creative  thought.  In  general- 
ity, comprehensiveness,  distinctness,  and  brevity  of 
statement  Kepler's  laws  are  equal  to  Newton's  ;  and  the 
great  advantage  of  the  latter  is  found  in  their  intellec- 
tual simplicity,  and  therefore  presumed  nearer  accord- 
ance with  the  way  in  which  the  Divine  Mind  sees  the 
planetary  motion.  The  test  of  ethical  and  political 
theories  is  their  conformity  to  the  will  of  God.  The 
ethical  judgments  are  drawn  with  such  instinctive 
rapidity  that  we  are  unconscious  of  their  bases.  But 
when  the  reflective  age  comes,  and  the  young  man 
begins  to  question  why  this  action  should  be  wrong, 
and  that  right ;  it  will  be  a  great  danger  to  his  in- 
tegrity and  virtue,  if  he  has  no  faith  in  the  being  of 
One  all-seeing,  all-holy,  just,  and  righteous  Judge, 
guiding  and  controlling  the  destinies  of  men. 


THEOLOGY.  1 47 

And,  as  a  merely  intellectual  idea,  there  is  no 
other  fitting  end  of  the  study  of  the  lower  branches  of 
the  hierarchy  than  the  recognition  of  the  wisdom  and 
goodness  of  the  Creator.  Those  modern  European 
writers  who  think  that  Theism  is  an  inferior 
system  to  Pantheism,  because  it  is  the  system  of 
the  Semitic  races,  who  are  inferior  to  the  Japhetic, 
are  as  mistaken  in  their  intellectual  conceptions  of 
science,  as  in  their  prejudice  of  race.  Physical  science 
is  the  unfolding  of  the  harmony  of  the  creative 
thoughts  ;  and  Mathematical  Science  derives  its  value 
from  its  furnishing  means  by  which  we  demonstrate 
that  harmony. 

I  have  been  acquainted  with  two  distinguished  teach- 
ers, who  conscientiously  abstained  from  giving  to  their 
pupils  their  own  opinions  concerning  religion  ;  they 
seemed,  in  regard  to  theology,  to  value  freedom  above 
truth  ;  and  would  rather  have  their  pupils  fall  into  error, 
than  to  exert  the  slightest  influence  over  them,  to  bias 
them.  It  seemed  to  me  a  mistaken  course,  and  I  think 
that  in  both  cases,  it  had  adisastrous  effect  on  the  pupils. 
Irreligious  and  sceptical  men,  and  sceptically  inclined 
young  people,  will  interpret  such  silence  as  disbelief 
in  religion  ;  and  the  teacher  does  thus  bias  the  minds 
of  some  of  his  pupils  towards  unbelief.  I  respect  a 
man  who  earnestly  fights  the  principles  of  Newton  as 
erroneous,  more  than  I  can  one  who  evades  your 
questions,  and  tells  you  that  he  does  not  wish  to  say 
whether  he  believes  or  disbelieves  the  results  of 
science.  I  should  prefer  an  outspoken  atheistic, 
materialistic  opponent  to  Christianity,  if  I  thought  him 


148  TRUE  ORDER  OF  STUDIES. 

really  honest,  to  a  man  who  was  unwilling  to  give 
up  the  name  of  Christian,  but  even  more  unwilling 
to  let  his  pupils  know  his  opinion  concerning  any  point 
of  natural  theology,  or  of  revealed  religion,  or  of  the 
evidences  of  Christianity. 


SCHOLIA.  149 


CHAPTER  XXII. 

SCHOLIA. 

/^  I  ^HE  teacher  must  not  forget  that  the  education 
-^  of  the  knowing  faculties,  is  a  very  imperfect 
and  unimportant  culture,  unless  we  at  the  same  time 
time  impart  the  power  of  expression  and  of  action,  and 
awake  sentiments  and  feelings  worthy  to  be  expressed 
or  embodied.  In  this  little  volume  we  have  been 
chiefly  occupied  in  showing  in  what  manner  we  con- 
ceive the  circle  of  human  sciences  to  be  bound  to- 
gether in  an  ascending  spire  ;  which  is  our  best  guide 
in  choosing  subjects  for  intellectual  instruction.  But 
the  body  also  needs  care  ;  the  teacher  and  the  parent 
should  see  to  it,  that  the  child  has  fresh  air,  of  proper 
temperature :  sufficient  muscular  exercise,  and  train- 
ing of  the  muscles  ;  good  and  wholesome  food,  and 
abstinence  from  what  is  hurtful;  sunshine  and 
cheerful  amusement.  The  heart  needs  training,  and 
the  teacher  and  the  parent  must  ever  by  the  example 
of  reverence,  kindness,  good  humor,  patience,  hope- 
fulness, appreciation  of  the  beautiful  and  the  true,  be 
cultivating  right  affections.  Above  all  the  will  needs 
training,  to  prompt  unhesitating  action  in  obedience, 
first  to  rightful  authority  on  earth  ;  then  to  the  will  of 
God,  in  heartfelt  consecration  to  his  service,  and  in 


150  TRUE  ORDER  OF  STUDIES. 

charity  to  men.  The  power  of  expression  and  action 
IS  ro  DC  cultivated  in  every  direction,  pursuing  ever^ 
scientific  study,  also,  first  of  all  as  an  art ;  both  for 
its  use  as  an  art,  and  for  the  superiority  of  the  mode 
of  approaching  it  as  a  science. 

And  we  believe  that  the  sequence  of  intellectual 
studies  which  we  have  endeavored  to  show  is  con- 
formed to  the  nature  of  things  and  to  the  nature  of  the 
growing  mind,  will  give  also  the  best  opportunity  for 
education  in  character  and  in  executive  ability.  For 
example,  we  place  first  in  the  scale  of  studies,  the  cul- 
tivation of  the  powers  of  observation  by  the  outward 
senses ;  before  invention  or  reasoning.  This  intel- 
lectual order  gives  the  opportunity,  in  the  case  of  the 
child's  body,  for  keeping  him  much  out  of  doors, 
rambling  under  the  guidance  of  its  teacher ;  by  the 
roadside,  or  over  the  pastures,  to  the  benefit  of  its 
health,  as  much  as  of  its  mind.  The  same  order  gives 
in  moral  education,  the  opportunity  for  developing 
pure  tastes,  and  a  love  of  natural  beauty  ;  it  affords, 
also,  social  pleasures  of  a  higher  character  than  the 
ordinary  plays  of  the  school-yard.  It  gives,  further- 
more, the  best  opportunity  for  impressing  the  young 
heart  with  a  sense  of  the  infinite  wisdom  and  love 
manifested  in  the  creation  ;  while  the  freedom  of  the 
walk  allows  the  child  to  manifest  its  character  in  its 
treatment  of  its  schoolmates  ;  and  gives  the  skilful 
teacher  opportunities  to  influence  it  to  active  kind- 
ness, thoughtfulness,  and  helpfulness. 

The  complaint,  so  urgently  made  by  some,  that  an 
intellectual  education  is  a  moral  injury  rather  than  a 


SCHOLIA.  151 

moral  benefit,  has  been  abundantly  shown  by  statistics 
to  be  without  adequate  foundation.  So  far  as  it  has 
any  foundation,  it  is  grounded  chiefly  upon  facts 
arising  out  of  the  inverted  order  of  our  intellectual 
drill ;  teaching  reasoning  rather  than  observation  • 
takins:  the  child's  attention  from  God's  book  of  nature 
to  fix  it  on  books  written  by  inferior  men  ;  making 
intellectual  training  so  difficult  and  discouraging  as  to 
interfere  with  the  time  and  strength  and  heart  for 
moral  training. 

In  like  manner,  the  injury  sometimes  done  to  the 
bodily  health  of  students,  by  over  exertion  of  the  brain, 
comes  in  no  small  degree,  from  the  unnatural  order  of 
studies,  giving  the  abstract  before  the  concrete  ;  by 
virtue  of  which  the  difficulties  of  each  step  are  greatly 
increased  ;  and  it  frequently  becomes  necessary  for 
the  student  to  master,  in  a  hurried  manner,  in  a  few 
months,  that  which,  under  the  natural  order  of  studies, 
he  would  have  acquired  leisurely  and  pleasurably, 
years  before.  Whatever  be  the  amount  of  knowledge 
acquired  in  a  given  time,  the  ease  of  its  acquisition, 
and  the  case  with  which  it  can  be  applied  to  use,  will 
be  partly  proportional  to  the  lucidness  and  naturalness 
of  the  order  in  which  its  parts  were  arranged  and  pre- 
sented to  the  student.  This  purely  intellectual  ques- 
tions, therefore,  of  the  true  order  of  studies  is  inti- 
mately connected,  in  more  than  one  mode,  with  all 
questions  that  involve  the  highest  welfare  of  the  indi- 
vidual, and  of  the  family,  of  the  State  and  of  the 
Church. 

Whether    I    have   made   any   contribution    toward 


152  TRUE  ORDER  OF  STUDIES. 

settling  the  question  in  what  order  the  studies  of  the 
curriculum  ought  to  be  placed,  or  not,  the  reader  must 
judge.  August  Comte  classified  the  branches  of 
knowledge  according  to  the  degree  of  generality  of 
their  ideas,  placing  mathematics  first,  because  the 
laws  of  form  and  number  govern  all  matter  in  the 
solar  system  ;  and  political  economy  last,  because  its 
laws  govern  only  about  one  million  tons  of  matter,  in 
the  form  of  human  brains  ;  psychology  and  theology 
he  remanded  to  the  realms  of  fable.  Herbert  Spencer 
denies  that  the  sciences  can  be  arranged  in  any  one 
series  ;  but  arranges  them  in  two.  or  more,  making 
the  sequence  in  each  series  depend  not  upon  the 
generality,  but  upon  the  abstractness  of  the  ideas  in- 
volved in  the  sciences.  Thus  he  also  places  the 
mathematics  first  because  they  are,  in  his  view,  the 
most  abstract.  Other  writers  have  classified  the  ob- 
jects of  study  more  or  less  thoroughly.  But  in  what- 
ever manner  our  philosophy  leads  us  to  classify  the 
branches  of  human  knowledge  ;  and  whether  we  do, 
or  do  not,  see  a  universal  order  and  arrangement  such 
as  I  have  given  as  the  hierarchy  of  sciences  ;  this  one 
point  I  would  press  upon  the  reader  as  certainly  true, 
and  of  great  practical  moment,  viz.  :  that  in  a  great 
many  cases,  notably  in  mathematics  and  physics,  there 
is  a  natural  order  in  which  they  should  be  taken  up, 
and  that  the  neglect  of  this  order,  so  common  in  our 
schools  and  colleges,  involves  a  great  waste  of  the 
student's  time  and  power,  and  cripples  his  usefulness 
in  after  life. 

While  all  the   studies  of  the  curriculum  must  be 


SCHOLIA.  153 

used  as  means  of  guiding  and  developing  the  power  of 
action  and  expression,  as  well  as  of  thought,  it  must 
especially  be  remembered  that  the  historical  studies, 
(trades,  arts,  language  and  law)  are  peculiarly  adapted 
to  this  function;  and  the  teacher  must  be  careful  to 
make  them  all  conspire  in  giving  the  pupil  freedom 
and  power  in  utterance ;  by  the  lips,  by  the  pen,  by 
the  fine  arts,  by  right  action.  Intellectual  thought 
finds  utterance  in  words  ;  sentiment  in  art ;  principle, 
in  acts.  Action  strengthens  principle,  gives  depth  to 
sentiment,  and  clearness  to  the  intellectual  vision. 

To  recapitulate  ;  I  see  the  objects  of  human 
thought  and  knowledge  arrange  themselves  in  five 
great  groups.  Under  the  first  come  Space  and  Time, 
and  the  abstract  idea  of  Number ;  concerning  these, 
men  build  the  sciences  of  Geometry,  Arithmetic, 
Algebra,  and  higher  mathematics.  Under  the  second 
lies  matter,  the  physical  universe  in  all  forms ;  con- 
cerning which  we  have  sciences  of  mechanics,  with 
its  remote  branches  of  acoustics,  thermotics,  optics,  &c., 
chemistry,  physiology,  botany,  zoology,  geology,  astron- 
omy, &c.  The  third  group  is  historical,  and  embraces 
all  that  man  has  said  or  done  on  this  planet ;  his 
manufactures,  commerce,  agriculture,  government, 
war,  literature,  fine  arts,  &c.  The  fourth  group  takes 
in  the  mental,  and  spiritual  powers  of  man ;  and  con- 
siders his  capacity  for  thought,  for  passion  and  senti- 
ment, and  for  actions  what  the  powers  are,  and  how 
limited  and  modified.  The  fifth  group  embraces  all 
the  attempts  which  man  has  made  to  rise  to  a  knowl- 
edge of  the  ultimate  causes  of  things,  the  origin  of  the 

7* 


154  TRUE    ORDER    OF    STUDIES. 

Universe,  the  mystery  of  the  government  of  all  the 
phenomena  by  noumena, — the  reign  of  law,  which  law 
is  thought. 

These  five  great  branches  appear  to  be  logically 
dependent  in  the  order  in  which  I  have  placed  them  ; 
geometry  being  the  foundation  of  learning ;  nor  can 
we  conceive  a  man  gaining  a  knowledge  of  anything 
whatever,  except  geometry,  until  he  has  gained  the 
corresponding  foundations  of  his  knowledge  in  each 
of  the  groups  below,  down  until  he  reaches  the  knowl- 
edge of  relations  in  space. 

The  order  of  the  hierarchy  is  the  logical  order  in 
which  the  sciences  are  developed  one  after  the  other, 
but  it  by  no  means  follows  that  mathematics  can 
be  developed  and  followed  to  their  highest  sum- 
mit without  reference  to  any  thing  that  succeeds. 
There  is  such  a  mutual  inter-dependence  that  the 
lower  branches  are  continually  suggested  by  the 
higher  ;  and  in  any  one  study,  we  not  only  require 
a  competent  knowledge  of  the  lower  branches,  to  en- 
able us  to  stand  where  we  are,  but  we  must  attempt 
to  use  our  knowledge  upon  a  higher  branch,  in  order 
to  receive  any  impulse,  to  rise  higher  in  the  one  upon 
which  we  stand.  Thus  the  mathematics  were  stimu- 
lated and  enlarged  by  the  attempt  to  apply  them  to 
mechanics  and  crystallography,  and  these  again 
stimulated  by  the  attempt  to  apply  them  to  chemistry. 
Chemistry  saw  new  fields  when  she  sought  to  solve 
the  problems  of  physiology ;  and  thus  on  through  the 
whole  of  the  sacred  circle. 

For    a  full   harmonious  development  of  a  child's 


SCHOLIA.  155 

mind  we  must  daily  recur  to  the  five  essential  branches 
of  inquiry  suggested  by  every  sight  of  nature.  The 
youngest  child  brings  in,  for  example,  a  dandelion. 
Its  circular  form,  its  radiant  lines,  the  number  of  its 
rays,  the  bell  shape  of  the  involucre,  the  cylindrical 
scape,  and  its  cylindrical  cavity,  the  close  spiral  into 
which  the  split  end  of  the  scape  curls  itself,  these 
are  mathematical  points  to  which  his  attention  may 
easily  be  directed.  Its  yellow  color,  slightly  bitter 
taste,  the  use  of  its  root  in  medicine,  and  in  the 
adulteration  and  imitation  of  coffee,  its  relationship  to 
asters,  sunflowers,  ox-eye  daisies,  fleabane,  tansy, 
yarrow,  ragweed, — these  matters  belong  to  the  great 
group  of  natural  history ; — in  some  of  them  the 
youngest  child  can  be  interested,  and  in  all  of  them 
the  older  ones.  The  derivation  of  the  name, 
dandelion  (dents  de  lion,  dens  leonis)  from  the 
form  of  the  green  leaf  ;  and  of  the  generic  name, 
taraxacum,  from  its  medical  effects  ;  the  fact  of  its 
introduction  from  Europe  ;  quotations  from  Lowell, 
and  other  poets,  referring  to  it ;  these  would  be 
historical  instructions  naturally  flowing  from  the 
incident  of  the  dandelion  being  brought  into  the 
schoolroom.  If  now  the  child  is  asked  why  he  likes 
the  flower  so  much ;  whether  it  is  because  it  is 
prettier  than  others  ;  or  whether  because  it  comes  so 
early  in  the  Spring  ;  or  whether  because  it  is  so  com- 
mon, the  poor  man's  flower,  and  the  children's  flower; 
the  questions  will  stimulate  a  healthy  psychological 
curiosity,  not  a  morbid  introversion,  but  held  still  to  a 
healthy  attitude  by  its  external   hold  upon  the  flower. 


10  TRUE    ORDER    OF    STUDIES. 

And  finally  this  little  flower  may  give  theological 
lessons  of  great  value,  if  without  parade  or  cant,  but 
in  a  simple  and  natural  manner,  you  allude  as  from 
your  own  fulness  of  heart,  to  the  goodness  of  the 
Heavenly  Father,  in  spreading  beauty  with  so  un- 
sparing a  hand  ;  or  simply  bringing  to  the  child's  re- 
membrance, by  quotation,  or  by  a  child  like  para- 
phrase, the  Saviour's  appeal  to  our  consciences,  drawn 
from  the  lily  of  the  field. 

Now  every  lesson,  in  this  school  of  life,  will  lead, 
as  naturally  as  this  dandelion  has  done,  to  the  five 
great  branches  of  intellectual  studies  ;  and  no  lesson 
has  done  its  full  work  for  our  minds  until  it  has  been 
thus  linked  into  relation  with  all  the  main  lines  of  de- 
pendent truth.  The  simplest  geometry  has  its  appli- 
cation to  physics ;  its  history  of  discovery  and  appli- 
cation ;  its  psychological  questions  of  the  foundations 
of  belief,  and  the  nature  of  proof ;  its  theological 
aspect,  in  the  query  for  example  whether  the  relations 
of  space  are  dependent  on  the  nature  of  our  minds,  and 
thus  upon  the  will  of  the  Creator.  The  cycle  of  the 
five  branches  must  thus  be  daily  recurring,  and  my 
aim  in  these  chapters  has  been  to  show  in  what  order 
the  five  branches  are  to  be  placed  ;  which  must 
always  precede,  and  which  follow  ;  which  must  always 
be  in  a  higher  state  of  development  ;  and  which,  the 
crown  and  glory  of  the  whole,  must  always  lie  least 
within  the  reach  of  our  finite  faculties. 

The  highest  truths  which  rnan  can  possibly  seek 
are  those  which  directly  pertain  to  the  unlimited 
Power,  the  unfathomable  Wisdom,  the  inexhaustible 


SCHOLIA.  157 

Love,  out  of  which  the  wondrous  spectacle  of  the 
Universe,  and  we,  as  spectators  and  actors  therein, 
ever  flow  ;  the  knowledge  of  these  truths  is  Theology. 
The  next  subject  in  dignity  and  importance  is  the 
investigation  of  our  own  souls,  whose  thoughts  and 
emotions,  and  holiest  sentiments,  we  see  prefigured 
and  pre-embodied  in  nature  ;  and  it  is  by  that  pre- 
sence of  a  likeness  within  us  to  the  creative  energies, 
that  we  are  able  partly  to  comprehend  the  created 
universe.  The  study  of  the  human  mind,  the  greatest 
work  of  God  known  to  us  is  Psychology.  Thirdly,  in 
our  inquiries,  we  ask  what  our  fellow  men  have 
thought,  and  said,  and  done,  on  this  theatre  of  the 
earth ;  and  the  answer  to  these  inquiries  we  call 
history.  Fourthly,  we  ask  concerning  the  other  acts 
of  the  Creator,  known  to  us,  beside  the  creation  of 
human  spirits  ;  we  inquire  concerning  this  universe 
of  matter  which  He  has  made, — and  trust  that  it  is 
not  irreverent  to  call  the  answer  to  our  inquiries 
Natural  History.  Finally,  our  attention  is  directed  to 
the  Universe  of  Space  and  Time,  in  which  the  realm 
of  matter  floats,  and  to  which  our  spirits  are  tied  by 
our  material  bodies  ;  but  the  relation  of  which  either 
to  the  finite  or  the  Infinite  Spirit,  is  beyond  our  grasp. 
And  the  truths  of  space  and  time  which  we  are 
taught,  we  call  mathematics. 

In  the  following  Curriculum,  I  lay  out  the  plan  of 
studies  for  an  ideal  course  of  liberal  education  ;  laid 
out  as  within  the  reach  of  the  majority  of  pupils,  as  I 
have  known  them  in  a  long  acquaintance  with  public 


158  TRUE  ORDER  OF  STUDIES. 

schools  in  our  country.  But  it  must  be  borne  in  mind 
by  him  who  would  examine  and  criticise  that  course 
of  studies,  that  it  has  a  unity  from  beginning  to  end  ; 
and  that  the  work  of  the  later  years  will  be  impractic- 
able for  scholars  who  have  not  had  the  earlier  trainins; 
here  prescribed. 


A   CURRICULUM.  1 59 


CHAPTER  XXIII. 

A    CURRICULUM. 

I.  Alphabet,  or  Sub-primary  School. 
For  childj'en  Jive  to  eight  years  old. 

1.  Mathematics. — Building  with  little  bricks,  and 
blocks,  playing  with  geometrical  puzzles  or  tangrams, 
drawing  geometrical  figures  ;  counting  beans,  and 
grouping  them  ;  keeping  time  in  music,  afterwards 
learning  the  Arabic  figures. 

2.  Natural  History. — Equilibrium,  and  breaking 
joints  in  their  block  buildings,  gathering  and  naming 
stones,  plants  and  insects  ;  afterwards  learning  the 
names  of  their  own  limbs  and  bones  ;  and  the  simp- 
lest facts  of  geography  illustrated  by  a  globe,  rectified 
in  the  actual  sunshine. 

3.  History. — Singing  by  rote,  and  afterwards  by 
note  ;  phonetic  analysis  of  words,  reading  phonotype, 
and  in  the  last  year  common  print.  Drawing  from 
copies  and  natural  objects.  Careful  subjection  to  the 
rules  of  the  school,  and  incidental  instruction. 

4.  Psychology. — Very  little  and  purely  incidental. 

5.  Theology. — Incidental,  from  presence  at  devot- 
ional exercises,  &c. 


lOO  TRUE  ORDER  OF  STUDIES. 

II.  Primary  School. 
For  children  from  eight  to  eleveji  years  old. 

1.  Mathematics. — Theorems  of  geometry  as  facts, 
without  reasons.  Drawing.  The  four  simple  rules  of 
written  arithmetic,  in  whole  numbers  and  decimals, 
practised  as  an  art,  not  studied  as  a  science.  Keeping 
time  in  music. 

2.  Natural  History . — Incidental  instruction  on  the 
sensible  properties  of  body,  degrees  and  kinds  of  hard- 
ness, elasticity,  fluidity,  etc.  Afterwards  on  rust,  com- 
bustion, soap  making,  fermentation,  etc.  Examination 
of  minerals,  plants  and  animals,  and  learning  to  recog- 
nize them.     Geography  from  the  globe. 

3.  History. — Visits  to  shops,  farms,  factories,  &c. 
Draw,  sing,  and  begin  on  the  piano  if  convenient,  at 
home.  Reading  and  writing,  both  common  hand  and 
phonography  ;  keeping  in  short-hand  a  brief  diary  ; 
and  writing  in  long  hand  letters  to  other  children 
and  little  stories.  Oral  instruction  in  History  of  the 
United  States. 

4.  Psychology. — As  before, 

5.  Theology. — Incidental  instruction  directed  chief- 
ly to  cultivation  of  a  reverent  and  devout  spirit,  rather 
than  to  any  theological  opinions. 

III.  Grammar  School. 
For  children  from  eleven  to  fourteen  years  old. 
I.  Mathematics. — Plane   geometry.       Mental  and 


A    CURRICULUM.  l6l 

written  arithmetic,  except  evolution.       Use   of   log- 
arithms. 

2.  Natural  History. — Astronomy  in  simple  form. 
Physical  geography,  maps.  Elementary  mechanics. 
Incidental  chemistry.     Botany,  zoology,  anatomy. 

3.  History. — Oral  accounts  of  inventions,  and  dis- 
coveries. Continue  drawing  and  singing,  introducing 
landscape,  and  part-singing.  Commit  to  memory 
selections  from  the  best  poetry.  Read  French  with- 
out grammar  or  dictionary.  Towards  the  close,  learn 
the  parts  of  speech,  and  take  the  elements  of  grammar. 
Continue  the  History  of  the  United  States,  and  begin 
that  of  England  and  the  Jews. 

4  and  5.  Psychology  and  Theology. — As  before,  the 
incidental  instruction  being  based  partly  now  upon 
the  readings  from  the  Bible. 

IV.  High  School. 

For  scholar's  from  fourteen  to  seventeen  years  old. 

1.  Mathematics. — Solid  geometry,  algebra,  trigono- 
metry and  its  applications.  Brief  review  of  arith- 
metic, with  evolution,  and  practice  in  logarithms.  An- 
alytic geometry.  For  scholars  of  higher  ability,  the 
rudiments  of  calculus,  and  of  quaternions,  orally 
imparted. 

2.  Natural  History. — Elements  of  acoustics,  op- 
tics and  thereotics.  Physical  geography.  Geology. 
Elements  of  Chemistry,  electricity  and  magnetism 
Physiology,  botany  and  zoology. 


l62  TRUE  ORDER  OF  STUDIES, 

3.  History. — History  of  agriculture,  manufactures^ 
and  commerce.  Drawing  and  music.  Continue  to 
read  French  as  before,  and  take  up  the  study  of  Latin. 
Afterwards  read  German  as  you  did  the  French,  and 
take  up  the  rudiments  of  Greek.  Take  successively 
histories  of  England  and  of  Greece,  and  Rome.  Con- 
stitution of  the  United  States,  with  oral  instruction  on 
constitutional  law. 

4.  PsycJiology. — Begin  elements  of  intellectual 
philosophy,  criticism,  and  ethics. 

5.  Theology. — The  incidental  instruction,  from  the 
Bible  reading  and  from  history,  may  become  more 
full  and  explicit. 

V.  College. 

For  scholars  from  seventeen  to  twenty-one  years  old. 

1.  Mathematics. — (Only  for  those  of  mathematical 
ability). — Analytic  geometry  as  affected  by  the  calcu- 
lus. Elements  of  more  modern  inventions,  quaternions, 
stigmatics,  kinematics,  etc.  Lectures  on  the  methods 
of  the  mathematics. 

2.  Natural  History. — (Reserved  for  those  of 
special  taste  for  these  studies). — Analytical  mechanics, 
applied  to  optics,  thermotics,  astronomy,  etc.,  etc. 
Chemistry,  botany,  zoology,  geology. 

3.  History. — Political  economy,  rhetoric.  Writing 
on  themes.  Extemporaneous  debate.  Declamation  of 
the  student's  own  writing.  Constitutional  law.  His- 
tory of  the  Greeks,   Romans,  Jews  and  English.     For 


A  CURRICULUM,  I63 

those  of   special   tastes,   Music  and  other  arts ;    or 
languages,  and  philology. 

4.  Psychology. — Metaphysics,     logic,     aesthetics, 
ethics. 

5.  Theology. — Natural     theology,     evidences     oi 
Christianity. 


THE   END. 


■^vr,\•T^/• 


University  of  California  Library 
Los  Angeles 

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